Inclusion Criteria:

          -  Pathologically (histologically or cytologically) proven diagnosis of NPC that has
             recurred at locoregional and/or distant sites. For locoregional recurrence, the
             disease must not be amenable to potentially curative surgery or re-irradiation. The
             following histological types are accepted: (a) Keratinizing - squamous cell carcinoma;
             (b) Non-keratinizing - undifferentiated or poorly differentiated

          -  Measurable disease by the RECIST 1.1 criteria. Lesion(s) that have been irradiated
             previously can be counted as measurable as long as radiological progression has been
             demonstrated prior to enrollment

          -  History/physical examination by a medical oncologist or clinical oncologist within 14
             days prior to registration

          -  Zubrod/Eastern Cooperative Oncology Group (ECOG) performance status of 0-1 within 14
             days prior to registration

          -  Contrast enhanced magnetic resonance imaging (MRI) or computed tomography (CT) of the
             nasopharynx and neck within 30 days prior to registration

          -  Contrast enhanced CT scan of the chest, abdomen, and pelvis within 30 days prior to
             registration

          -  Absolute neutrophil count (ANC) >= 1500 cells/mm^3 (within 14 days prior to
             registration)

          -  Platelets >= 100,000 cells/mm^3 (within 14 days prior to registration)

          -  Hemoglobin >= 9.0 g/dL (transfusion is accepted. Erythropoietin dependency not
             accepted) (within 14 days prior to registration)

          -  Total bilirubin =< 1.5 x upper limit of normal (ULN) OR direct bilirubin =< ULN for
             patients with total bilirubin levels > 1.5 x ULN. Patients with known Gilbert's
             syndrome are not excluded (within 14 days prior to registration)

          -  Alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase [SGPT]) =< 2.5 x
             ULN (=< 3 x ULN for patients with liver metastases) (within 14 days prior to
             registration)

          -  Serum creatinine =< 1.5 x ULN OR calculated creatinine clearance (CrCl) based on
             Cockcroft-Gault equation >= 30 mL/min for patients with serum creatinine levels > 1.5
             x ULN. In this protocol, cisplatin or carboplatin may be used at the discretion of the
             investigator - except for patients with CrCl between 30-50 mL/min, for whom
             carboplatin should be used instead of cisplatin (within 14 days prior to registration)

          -  For patients with evidence of chronic hepatitis B virus (HBV) infection, the HBV viral
             load must be undetectable, and patients must be receiving anti-viral therapy at
             enrollment. Patients must agree to continue anti-viral therapy throughout the study
             period as directed by their treating physicians

               -  Known positive test for hepatitis B virus surface antigen (HBsAg) indicating
                  acute or chronic infection would make the patient ineligible unless the viral
                  load becomes undetectable on anti-viral therapy

               -  Patients who are immune to hepatitis B (anti-Hepatitis B surface antibody
                  positive) are eligible (i.e., patients immunized against hepatitis B)

               -  In some centers, hepatitis B core antibody (anti-HBc) is done routinely before
                  chemotherapy for some cancer patients. This is because patients who are
                  HBsAg-negative but positive for anti-HBc should have undetectable HBV viral load
                  at enrollment and receive prophylactic anti-viral therapy throughout the study
                  (American Society of Clinical Oncology 2015 guideline, Hwang 2015). In this
                  protocol, anti-HBc should be performed based on institutional standards

          -  Patients with a history of hepatitis C virus (HCV) infection must have been treated
             and cured. For patients with HCV infection who are currently on treatment they are
             eligible if they have an undetectable HCV viral load

               -  Note: Known positive test for hepatitis C virus ribonucleic acid (HCV RNA)
                  indicating acute or chronic infection would make the patient ineligible unless
                  the viral load becomes undetectable on suppressive therapy

          -  For women of childbearing potential (WOCBP), negative serum or urine pregnancy test
             within 14 days prior to registration. For WOCBP randomized to Arm 1, an additional
             negative serum or urine pregnancy is required within 24 hours prior to starting
             nivolumab treatment

               -  Women of childbearing potential (WOCBP) is defined as any female who has
                  experienced menarche and who has not undergone surgical sterilization
                  (hysterectomy or bilateral oophorectomy) or who is not postmenopausal. Menopause
                  is defined clinically as 12 months of amenorrhea in a woman over 45 in the
                  absence of other biological or physiological causes

          -  Women of childbearing potential (WOCBP) and men who are sexually active with WOCBP
             must be willing to use an adequate method of contraception. Women must use an
             effective oral contraception and the male partner must use condom) during and after
             treatment

          -  The patient or a legally authorized representative must provide written informed
             consent prior to study entry

        Exclusion Criteria:

          -  Diagnosed with another invasive malignancy (except non-melanomatous skin cancer)
             unless disease free for more than 3 years. Note: Patients with basal cell carcinoma of
             the skin, squamous cell carcinoma of the skin, or carcinoma in situ (e.g. breast
             carcinoma, cervical cancer in situ) who have undergone potentially curative therapy
             are not excluded

          -  Any prior systemic anti-cancer agents (including chemotherapy and investigational
             agents) for the purpose of treating locoregional and/or distant recurrence of NPC

          -  Patients who have received neoadjuvant (induction) and/or adjuvant chemotherapy for
             primary NPC with chemotherapy (any drug regimens including those containing platinum
             and/or gemcitabine) at or within 6 months prior to registration are excluded (counting
             from the last day of the chemotherapy for the primary NPC, prior to enrolling into the
             current study). The following subgroups of patients are NOT excluded:

               -  Patients who have received neoadjuvant (induction) and/or adjuvant chemotherapy
                  for primary (non-metastatic/non-recurrent) NPC more than 6 months prior to
                  registration, counting from the last day of the chemoradiotherapy for the primary
                  NPC, prior to enrolling into the current study

               -  For prior RT with radical intent: Patients who have prior radiotherapy (RT) to
                  the primary and locoregional disease (i.e. non-recurrent disease) with or without
                  concurrent cisplatin or carboplatin monotherapy are not excluded as long as they
                  have not received any neoadjuvant/adjuvant chemotherapy within 6 months prior to
                  registration (counting from the last day of the chemotherapy), and that the last
                  RT fraction (with radical intent) has been given more than 3 months prior to
                  registration

               -  For RT with palliative intent: Prior radiotherapy (RT) at or within 30 days prior
                  to registration, this includes RT given with palliative intent (with or without
                  concurrent cisplatin or carboplatin alone) to recurrent/ metastatic sites in
                  patients with recurrent/metastatic NPC. The re-irradiated sites must not be the
                  only sites of measurable recurrent disease

               -  Prior chemotherapy for cancers other than NPC is allowed as long as the last
                  course of chemotherapy was administered more than 3 years prior to registration
                  and the patient has remained disease-free for more than 3 years

          -  Prior therapy for any indication, with an anti-PD-1, anti-PD-L1, or anti-PD-L2 agent
             or with an agent directed to another stimulatory or co-inhibitory T-cell receptor
             (e.g. CTLA-4, OX-40, CD137)

          -  History of severe (grade 3-4) hypersensitivity reaction to any monoclonal antibody
             including nivolumab and/or any of its excipients

          -  Severe, active co-morbidity defined as follows:

               -  Unstable angina and/or congestive heart failure requiring hospitalization within
                  the last 6 months

               -  Myocardial infarction within the last 6 months

               -  Acute bacterial or fungal infection requiring intravenous antibiotics at the time
                  of registration

               -  Chronic obstructive pulmonary disease exacerbation or other respiratory illness
                  requiring hospitalization or precluding study therapy within 30 days of
                  registration

               -  Hepatic insufficiency resulting in clinical jaundice and/or coagulation defects

               -  History of (non-infectious) pneumonitis that required steroids or has current
                  pneumonitis requiring steroids and/or immunosuppressive therapy

               -  History of active TB (Bacillus tuberculosis, not known to be multi-drug
                  resistant) as defined by the need to receive systemic treatment within the last 2
                  years or any known history of multi-drug resistant TB. Note: Patients who had a
                  distant history of treated TB (not known to be multi-drug resistant) at 5 or more
                  years from enrollment and have no current symptoms suggestive of active TB, are
                  not excluded from this study. Note: Testing for prior exposure to TB is not
                  required in this study since TB is endemic in parts of Asia

               -  Prior solid organ transplant or bone marrow transplant

               -  History of active primary immunodeficiency including, but not limited to acquired
                  immune deficiency syndrome (AIDS) based upon current Centers for Disease Control
                  and Prevention (CDC) definition; Note: Human immunodeficient virus (HIV) testing
                  is not required for entry into this protocol. The need to exclude patients with
                  AIDS from this protocol is necessary because the treatment involved in this
                  protocol may be immunosuppressive

               -  Condition requiring systemic treatment with either corticosteroids (> 10 mg daily
                  prednisone or equivalents) or other immunosuppressive medications within 14 days
                  of registration. Inhaled or topical steroids and adrenal replacement doses < 10
                  mg daily prednisone equivalents are permitted in the absence of active autoimmune
                  disease. Steroid premedication for the prophylaxis of CT contrast-related
                  allergies is allowed. The use of dexamethasone as an anti-emetic premedication
                  prior to chemotherapy is also allowed

               -  Active autoimmune disease requiring systemic treatment (i.e. disease modifying
                  agents, corticosteroids, or immunosuppressive drugs) within the past 2 years.
                  These include but are not limited to patients with a history of immune-related
                  neurologic disease, multiple sclerosis, autoimmune (demyelinating) neuropathy,
                  Guillain-Barre syndrome, myasthenia gravis; systemic autoimmune disease such as
                  systemic lupus erythematosus (SLE), rheumatoid arthritis, connective tissue
                  diseases, scleroderma, inflammatory bowel disease (IBD), Crohn's, ulcerative
                  colitis, hepatitis; and patients with a history of toxic epidermal necrolysis
                  (TEN), Stevens-Johnson syndrome, or phospholipid syndrome should be excluded
                  because of the risk of recurrence or exacerbation of disease

               -  Note: Patients are permitted to enroll if they have vitiligo; type I diabetes
                  mellitus; hypothyroidism, pituitary or adrenal insufficiency requiring only
                  hormone replacement; psoriasis not requiring systemic treatment, or conditions
                  not expected to recur in the absence of an external trigger (precipitating event)

          -  Patients who are pregnant or breastfeeding and unwilling to discontinue breastfeeding

          -  Known history of grade 3-4 allergic reaction and/or hepatic toxicity to cisplatin,
             carboplatin, or gemcitabine

               -  NOTE: For patients with known history of grade 3-4 renal toxicity to cisplatin or
                  known history of clinically significant hearing loss (grade 2 or above)
                  attributed to cisplatin, or other intolerances to cisplatin that are of clinical
                  significance, carboplatin can be used in this study and therefore these patients
                  are NOT excluded from enrollment

          -  Known central nervous system (CNS) metastases and/or carcinomatous meningitis.
             Patients with base of skull involvement by NPC are not excluded unless their disease
             is directly invading the brain parenchyma and is associated with clinical symptoms
             (headaches, nausea and vomiting, neurological abnormalities on physical examination)
             and/or cerebral edema on radiological imaging

          -  Patients who have received a live vaccine within 30 days prior to the first dose of
             study treatment. Examples of live vaccines include, but are not limited to, the
             following: measles, mumps, rubella, varicella/zoster, yellow fever, rabies, Bacillus
             Calmette-Guerin (BCG), and typhoid vaccine. Seasonal influenza vaccines for injection
             are generally killed virus vaccines and are allowed; however, intranasal influenza
             vaccines (e.g., FluMist) are live attenuated vaccines and are not allowed

          -  History or current evidence of any condition, therapy, or laboratory abnormality that
             might confound the results of the study, interfere with the subject's participation
             for the full duration of the study, or is not in the best interest of the subject to
             participate, in the opinion of the treating investigator