Inclusion Criteria:

          -  Patients must have clinically and radiographically suspected International Federation
             of Gynecology and Obstetrics (FIGO) stage (Appendix 2) 3 or 4 high grade serous
             ovarian, primary peritoneal or fallopian tube cancer, high grade, for whom the plan of
             management will include neoadjuvant chemotherapy (NACT) with interval tumor reductive
             surgery (TRS). Patients will be selected for NACT according to established criteria
             (Society of Gynecologic Oncology and the American Society of Clinical Oncology
             Guideline, https://www.ncbi.nlm.nih.gov/pubmed/27650684). Patients must have undergone
             core needle biopsy for histologic confirmation prior to start of treatment. See
             Appendix 3 for guidelines to aid in histologic diagnosis.

          -  Institutional confirmation of pathology on or laparoscopic biopsy performed at MSKCC
             with sufficient tissue for analysis or willingness to undergo repeat laproscopic
             biopsy if diagnostic biopsy was performed at an outside hospital.

          -  Appropriate stage for study entry based on the following diagnostic workup:

               -  History/physical examination within 28 days prior to registration;

               -  CT imaging of the chest, abdomen and pelvis within 28 days prior to registration
                  documenting disease consistent with FIGO stage III or IV disease (patients who
                  cannot receive contrast may instead undergo MRI of abdomen and pelvis along with
                  non-contrast chest CT);

               -  Further protocol-specific assessments as detailed below.

          -  Age ≥18

          -  ECOG Status of 0, 1, or 2 within 28 days prior to registration.

          -  Adequate hematologic function within 14 days prior to registration defined as follows:

               -  ANC ≥1,000/mcl. This ANC cannot have been induced by granulocyte colony
                  stimulating factors.

               -  Platelets ≥75,000/mc

               -  Hemoglobin ≥8.0 mg/dl (transfusions are permitted to achieve baseline hemoglobin
                  level)

          -  Adequate renal function within 14 days prior to registration defined as follows:

             °Creatinine <=1.5 x ULN.

          -  Adequate hepatic function within 14 days prior to registration defined as follows:

               -  Bilirubin ≤ 1.5 x ULN

               -  ALT and AST ≤ 3 x ULN

               -  Alkaline phosphatase ≤ 2.5 x ULN

               -  For patients with Gilbert's syndrome, Bilirubin ≤ 3 xULN is acceptable.

          -  Neurologic function: Neuropathy (sensory and motor) less than or equal to CTCAE Grade
             1.

          -  Adequate thyroid function within 14 days prior to registration defined as serum TSH
             within the normal range.

          -  The patient or legally authorized representative must provide study-specific informed
             consent prior to study entry.

        Exclusion Criteria:

          -  Subjects with a history of other invasive malignancies, with the exception of
             non-melanoma skin cancer, are excluded if there is any evidence of other malignancy
             being present within the last 3 years. Subjects are also excluded if their previous
             cancer treatment contraindicates this protocol's therapy.

          -  Patients who have received prior radiotherapy to any portion of the abdominal cavity
             or pelvis or thoracic cavity within the last three years are excluded. Prior radiation
             for localized cancer of the breast, head and neck or skin is permitted, provided that
             it was completed more than three years prior to registration, and the patient remains
             free of recurrent or metastatic disease.

          -  Patients who have received any prior treatment for management of their epithelial
             ovarian, fallopian tube or peritoneal primary cancer.

          -  Patients with any histology other than high grade serous evident on pretreatment
             biopsy.

          -  Patients with synchronous primary endometrial cancer, or a past history of primary
             endometrial cancer, unless all of the following conditions are met: Stage not greater
             than I-A, grade 1 or 2, no more than superficial myometrial invasion, without vascular
             or lymphatic invasion; no poorly differentiated subtypes, including serous, clear cell
             or other FIGO grade 3 lesions.

          -  Severe, active co-morbidity defined as follows:

          -  Chronic or current active infectious disease requiring systemic antibiotics,
             antifungal or antiviral treatment (with the exception of uncomplicated UTI)

          -  Clinically significant cardiac disease including unstable angina, acute myocardial
             infarction within 6 months from enrollment, New York Heart Association Class III or IV
             congestive heart failure, and serious arrhythmia requiring medication (this does not
             include asymptomatic atrial fibrillation with controlled ventricular rate).

          -  Partial or complete gastrointestinal obstruction

          -  Patients with anticipated contraindications to interval tumor reductive surgery.

          -  Patients with any condition that in the judgment of the investigator would jeopardize
             safety or patient compliance with the protocol.

          -  Patients who are unwilling to be transfused with blood components.

          -  Concurrent anticancer non protocol directed therapy (e.g. chemotherapy, radiation
             therapy, biologic therapy, immunotherapy, hormonal therapy, investigational therapy).

          -  Receipt of an investigational study drug for any indication within 28 days or 5
             half-lives (whichever is longer) prior to Day 1 of protocol therapy.

          -  Patients who, in the opinion of the investigator, are unable or unlikely to comply
             with the dosing schedule and study evaluations.

          -  Patients who are pregnant or nursing. The effects of nivolumab on the developing human
             fetus are unknown. For this reason, women of child-bearing potential (WOCBP) must
             agree to use adequate contraception (hormonal or barrier method of birth control;
             abstinence) prior to study entry and for the duration of study participation. WOCBP
             must have a negative serum or urine pregnancy test within 7 days of study enrollment,
             prior to dosing nivolumab, then every 6 weeks. After discontinuation from nivolumab
             these should be repeated at approximately 30 days and approximately 70 days. Women
             must not be breastfeeding.

               1. Women who are not of childbearing potential (i.e., who are postmenopausal or
                  surgically sterile) do not require contraception.

               2. Women of childbearing potential (WOCBP) is defined as any female who has
                  experienced menarche and who has not undergone surgical sterilization
                  (hysterectomy and/or bilateral oophorectomy) or who is not postmenopausal.
                  Menopause is defined clinically as 12 month amenorrhea in a woman over 45 in the
                  absence of other biological or physiological causes. In addition, women under the
                  age of 55 must have a documented serum follicle stimulating hormone (FSH) level
                  greater than 40mIU/mL.

          -  Patients are excluded if they have active brain metastases or leptomeningeal
             metastases. Subjects with brain metastases are eligible if metastases have been
             treated and there is no magnetic resonance imaging (MRI) evidence of progression for 4
             weeks or more after treatment is complete and within 28 days prior to the first dose
             of nivolumab administration. There must also be no requirement for immunosuppressive
             doses of systemic corticosteroids (> 10 mg/day prednisone equivalents) for at least 2
             weeks prior to study drug administration.

          -  In order for patients with known history of testing positive for human
             immunodeficiency virus (HIV) or known acquired immunodeficiency syndrome (AIDS) to be
             eligible, they must be on a stable highly active antiretroviral therapy (HAART)
             regimen, have CD4 counts > 350, with no detectable viral load on quantitative PCR.

          -  Patients with treated hepatitis virus infections (Hepatitis B or Hepatitis C) are
             eligible if they have been definitively treated for 6 months, have no detectable viral
             load on quantitative PCR, and LFTs meet eligibility requirements.

          -  Patients with active autoimmune disease or history of autoimmune disease that might
             recur, which may affect vital organ function or require immune suppressive treatment
             including systemic corticosteroids, should be excluded. 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 SLE, connective tissue diseases,
             scleroderma, inflammatory bowel disease, 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. Patient with vitiligo, endocrine deficiencies including
             thyroiditis managed with replacement hormones including physiologic corticosteroids
             are eligible. Patients with rheumatoid arthritis and other arthropathies, Sjogren's
             syndrome and psoriasis controlled with topical medication and patients with positive
             serology, such as antinuclear antibodies (ANA), anti-thyroid antibodies should be
             evaluated for the presence of target organ involvement and potential need for systemic
             treatment but should otherwise be eligible.

          -  Patients are permitted to enroll if they have vitiligo, type I diabetes mellitus,
             residual hypothyroidism due to autoimmune condition only requiring hormone replacement
             (such as Hashimoto's thyroiditis), psoriasis not requiring systemic treatment, or
             conditions not expected to recur in the absence of an external trigger (precipitating
             event).

          -  Patients should be excluded if they have a condition requiring systemic treatment with
             either corticosteroids (>10 mg daily prednisone equivalents) or other
             immunosuppressive medications within 14 days of study drug administration. Inhaled or
             topical steroids and adrenal replacement doses <10 mg daily prednisone equivalents are
             permitted in the absence of active autoimmune disease. Patients are permitted to use
             topical, ocular, intra-articular, intranasal, and inhalational corticosteroids (with
             minimal systemic absorption). A brief course of corticosteroids for prophylaxis (e.g.,
             contrast dye allergy) or for treatment of non-autoimmune conditions (e.g.,
             delayed-type hypersensitivity reaction caused by contact allergen) is permitted.

          -  Any of the following within 2 months of registration: active peptic ulcer disease,
             diverticulitis, cholecystitis, symptomatic cholangitis or appendicitis, malabsorption
             syndrome. Any of the following within 6 months of registration: Intra-abdominal
             abscess, gastrointestinal obstruction requiring parenteral hydration and/or nutrition,
             gastrointestinal perforation. Note: complete resolution of an intra-abdominal abscess
             must be confirmed prior to registration even if the abscess occurred more than 6
             months prior to registration.