Inclusion Criteria:

          -  Patient must be between 18 and 79 years of age

          -  Patient must have locoregionally recurrent or second primary HNSCC (oral cavity,
             oropharynx, larynx, hypopharynx) in a previously radiated field

          -  Patient must have undergone surgery with gross total resection and must be randomized
             within 8 weeks of surgery

          -  Patients must have high risk disease defined as:

               -  Positive margins and/or extra nodal extension (ENE)

                    -  Positive margins are defined as malignancy at or within 1 mm of the margin.
                       High grade dysplasia (i.e. carcinoma in situ) at the margin is also
                       considered positive

                    -  ENE may be either gross or microscopic

          -  Patient must have a PD-L1 Combined Positive Score (CPS) >= 1 in a Clinical Laboratory
             Improvement Act (CLIA) certified laboratory. Testing can be done locally as long as it
             is done in a CLIA certified laboratory. This testing must be on the tumor specimen
             from the resection of the patient's recurrent or second primary HNSCC

          -  Patient must have had prior radiation to the area of recurrent or second primary
             tumor. This is defined as > 50% of the presurgical tumor volume having previously
             received a dose of > 45 Gy as determined by the treating radiation oncologist

          -  Patient must have completed prior radiation a minimum of 6 months prior to
             randomization

          -  Patient must have an Eastern Cooperative Oncology Group (ECOG) performance status 0-1

          -  Patient must have the ability to understand and the willingness to sign a written
             informed consent document. Patients with impaired decision-making capacity (IDMC) who
             have a legally authorized representative (LAR) or caregiver and/or family member
             available will also be considered eligible

          -  Women of childbearing potential and sexually active males must not expect to conceive
             or father children by using by using accepted and effective method(s) of contraception
             or by abstaining from sexual intercourse while on study treatment, and continue for
             120 days after the last dose of study treatment

          -  Absolute neutrophil count (ANC) >= 1,500/mcL (obtained =< 28 days prior to protocol
             randomization)

          -  Platelets >= 100,000/mcL (obtained =< 28 days prior to protocol randomization)

          -  Total bilirubin =< 1.5 x institutional upper limit of normal (ULN) (obtained =< 28
             days prior to protocol randomization)

          -  Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase
             [SGOT])/alanine aminotransferase (ALT) (serum glutamic pyruvic transaminase [SGPT]) =<
             3.0 x institutional ULN (obtained =< 28 days prior to protocol randomization)

          -  Creatinine clearance > 30 ml/min using the Cockcroft-Gault formula (obtained =< 28
             days prior to protocol randomization)

          -  Human immunodeficiency virus (HIV)-infected patients on effective anti-retroviral
             therapy with undetectable viral load within 6 months are eligible for this trial as
             long as they do not have a history of Kaposi sarcoma and/or Multicentric Castleman
             Disease

          -  Patients with known history or current symptoms of cardiac disease, or history of
             treatment with cardiotoxic agents, should have a clinical risk assessment of cardiac
             function using the New York Heart Association Functional classification. Patients with
             New York Heart Association class III or IV heart failure are not eligible

        Exclusion Criteria:

          -  Patient must not have any evidence of distant disease based on baseline imaging done
             28 days prior to randomization

          -  Patient must not have received anti-PD-1/PD-L1 therapy for recurrent disease. If the
             patient received anti-PD-1/PD-L1 therapy as part of initial upfront curative intent
             treatment (either as part of definitive non-surgical therapy or in the adjuvant
             setting) in the past, the last dosage of anti-PD-1/PD-L1 therapy must have been given
             greater than one year prior to randomization

          -  Women must not be pregnant or breast-feeding due to the potential harm to an unborn
             fetus and possible risk for adverse events in nursing infants with the treatment
             regimens being used. All females of childbearing potential must have a blood test or
             urine study within 14 days prior to randomization to rule out pregnancy. A urine or
             serum pregnancy test must be repeated within 72 hours prior to receiving the first
             dose of pembrolizumab or chemotherapy if the test done for eligibility/randomization
             is done outside of this 72 hour window. If the urine test is positive or cannot be
             confirmed as negative, a serum pregnancy test will be required. A female of
             childbearing potential is defined as any woman, regardless of sexual orientation or
             whether they have undergone tubal ligation, who meets the following criteria: 1) has
             achieved menarche at some point, 2) has not undergone a hysterectomy or bilateral
             oophorectomy; or 3) has not been naturally postmenopausal (amenorrhea following cancer
             therapy does not rule out childbearing potential) for at least 24 consecutive months
             (i.e., has had menses at any time in the preceding 24 consecutive months)

          -  Patient must not have a known history of hepatitis B (defined as hepatitis B surface
             antigen [HBsAg] reactive) infection

          -  Patient must not have known active hepatitis C virus (defined as hepatitis C virus
             [HCV] ribonucleic acid [RNA] [qualitative] is detected) infection.

               -  NOTE: No testing for hepatitis B and hepatitis C is required unless mandated by a
                  local health authority

          -  Patient must not have a current active infection that requires systemic treatment at
             time of randomization

          -  Patient must not have a history of non-infectious pneumonitis requiring steroids
             within 3 years prior to randomization

          -  Patient must not have a history of solid organ transplant or stem cell transplant

          -  Patient must not be on immunosuppressive medication within 7 days prior to
             randomization, EXCEPT for the following: a) intranasal, inhaled, topical steroids, or
             local steroid injection (e.g., intra-articular injection); b) systemic corticosteroids
             at physiologic doses =< 10 mg/day of prednisone or equivalent; c) steroids as
             premedication for hypersensitivity reactions (e.g., computed tomography [CT] scan
             premedication)

          -  Patient must not have received a live vaccine within 30 days prior to the first dose
             of study drug. Examples of live vaccines include, but are not limited to, the
             following: measles, mumps, rubella, varicella/zoster (chicken pox), 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

          -  Patient must not have severe hypersensitivity (>= grade 3) to pembrolizumab and/or any
             of its excipients

          -  Patient must not have an active autoimmune disease that has required systemic
             treatment in past 2 years (i.e., with use of disease modifying agents, corticosteroids
             or immunosuppressive drugs). Replacement therapy (e.g., thyroxine, insulin, or
             physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency)
             is not considered a form of systemic treatment and is allowed

          -  Patient must not have a known psychiatric or substance abuse disorder that would
             interfere with the participant's ability to cooperate with the requirements of the
             study