Inclusion Criteria:

          -  STEP 1 (REGISTRATION)

          -  Pathologically (histologically or cytologically) proven diagnosis of head and neck
             squamous cell carcinoma (HNSCC) involving the oral cavity (excluding lips), oropharynx
             (p16 negative), hypopharynx or larynx

          -  Patients must have undergone gross total surgical resection of high-risk oral cavity,
             oropharynx (p16 negative), larynx, or hypopharynx squamous cell carcinoma (SCC) within
             63 days prior to registration; note: patients may have a biopsy under general
             anesthesia in an operating room followed by definitive ablative cancer surgery
             representing gross total resection; the gross total resection has to be done within 63
             days prior to registration; if, however, patients have ablative resection but
             demonstrate rapid gross recurrence or are determined to have gross persisting disease
             requiring re-resection to achieve gross total resection, then the patient is not
             eligible

          -  Patients must have at least one of the following high risk pathologic features:

               -  Extracapsular nodal extension

               -  Invasive cancer at the primary tumor resection margin (tumor on ink); Note:
                  Patients who have a positive margin and undergo re-resection with final negative
                  margin are eligible only if they can be enrolled within 63 days of initial gross
                  total resection AND extracapsular nodal extension was also present; patients who
                  have a positive margin and undergo re-resection with final negative margin and do
                  not have extracapsular nodal extension, are NOT eligible

          -  Pathologic stage III or IV HNSCC, including no distant metastases, based on the
             following minimum diagnostic workup:

               -  General history/physical examination by a radiation oncologist and/or medical
                  oncologist within 84 days prior to registration

               -  Examination by an ear nose and throat (ENT) or head & neck surgeon prior to
                  surgery; a laryngopharyngoscopy (mirror and/or fiberoptic and/or direct
                  procedure), if appropriate, is recommended but not required; intra-operative
                  examination is acceptable documentation

               -  Pre-op Imaging of the head and neck: a neck computerized tomography (CT) (with
                  contrast) or CT/positron emission tomography (PET) (with contrast) and/or an
                  magnetic resonance imaging (MRI) of the neck (T1 with gadolinium and T2) within
                  84 days prior to surgery; note: this imaging data (diagnostic pre-operative scan
                  showing gross disease) is to be submitted in Digital Imaging and Communications
                  in Medicine (DICOM) format via transfer of images and data (TRIAD); the report is
                  to be uploaded into Rave

               -  Chest imaging with either a CT scan (with or without contrast) or CT/PET (with or
                  without contrast) that includes the chest within 120 days prior to registration;
                  Note: if the CT/PET with or without contrast is done within 84 days prior to
                  surgery, it fulfills the chest imaging requirement

          -  For patients with oropharyngeal cancer only: the institution will do p16 testing, and
             if p16 is negative, this tissue must be submitted for central review for confirmation
             before Step 2 registration; note: if the institution finds that the patient is p16
             positive, the patient is excluded from this trial on the basis of distinct biology,
             prognosis, and low- or intermediate-risk rather than high-risk status

          -  Zubrod performance status of 0-1 within 28 days prior to registration

          -  Absolute neutrophil count (ANC): >= 1,500 /mm^3

          -  Platelets: >= 100,000 / mm^3

          -  Hemoglobin: >= 8.0 g/dL (note: the use of transfusion or other intervention to achieve
             hemoglobin [Hgb] >= 8.0 g/dl is acceptable)

          -  Creatinine clearance (CrCl) >= 50 ml/min within 14 days prior to registration as
             determined by 24-hour collection or estimated by Cockcroft-Gault formula

          -  Serum total bilirubin: =< 1.5 X ULN OR

          -  Direct bilirubin: =< ULN for patients with total bilirubin levels > 1.5 ULN

          -  Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase [SGOT]) and
             alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase [SGPT]) =< 2.5 X
             ULN

          -  International normalized ratio (INR) or prothrombin time (PT): =< 1.5 X ULN unless
             patient is receiving anticoagulant therapy as long as PT or partial thromboplastin
             time (PTT) is within therapeutic range of intended use of anticoagulants

          -  Activated Partial Thromboplastin Time (aPTT): =< 1.5 X ULN unless patient is receiving
             anticoagulant therapy as long as PT or PTT is within therapeutic range of intended use
             of anticoagulants

          -  The following assessments are required within 14 days prior to registration: sodium
             (Na), potassium (K), chlorine (Cl), glucose, calcium (Ca), magnesium (Mg), and
             albumin; note: patients with an initial magnesium < 0.5 mmol/L (1.2 mg/dl) may receive
             corrective magnesium supplementation but should continue to receive either
             prophylactic weekly infusion of magnesium and/or oral magnesium supplementation (e.g.,
             magnesium oxide) at the investigator's discretion

          -  For women of childbearing potential, a negative serum pregnancy test within 14 days of
             registration

          -  Female patients of childbearing potential and men receiving MK-3475 (pembrolizumab)
             who are sexually active with women of childbearing potential must be willing to use an
             adequate method of contraception for the course of the study through 120 days after
             the last dose of MK-3475 (pembrolizumab); note: abstinence is acceptable if this is
             the usual lifestyle and preferred contraception for the patient

          -  Patients with feeding tubes are eligible for the study

          -  The patient or a legally authorized representative must provide study-specific
             informed consent prior to study entry, including consent for mandatory tumor tissue,
             serum, and blood submission for immune correlatives (all patients) and p16 analysis
             (oropharyngeal cases only)

          -  STEP 2 (REGISTRATION)

          -  For patients with oropharyngeal cancer only: p16 negative, confirmed by central
             pathology review

        Exclusion Criteria:

          -  Definitive clinical or radiologic evidence of metastatic disease

          -  Prior invasive malignancy (except non-melanomatous skin cancer) unless disease free
             for a minimum of 1095 days (3 years); noninvasive cancers (for example, carcinoma in
             situ of the breast, oral cavity, or cervix) are permitted even if diagnosed and
             treated < 3 years ago

          -  Patients with simultaneous primaries or bilateral tumors are excluded, with the
             exception of patients with bilateral tonsil cancers or patients with T1-2, N0, M0
             differentiated thyroid carcinoma, who are eligible

          -  Prior systemic therapy, including cytotoxic chemotherapy, biologic/targeted therapy,
             or immune therapy for the study cancer; note: prior cytotoxic chemotherapy or
             biologic/targeted therapy for a different cancer is allowable; however, a prior
             anti-programmed cell death (PD)-1, anti-PD-L1, or anti-programmed cell death 1 ligand
             2 (PD-L2) agent is not permitted

          -  Prior radiotherapy to the region of the study cancer that would result in overlap of
             radiation therapy fields

          -  Severe, active co-morbidity defined as follows:

               -  Unstable angina and/or congestive heart failure requiring hospitalization within
                  6 months prior to registration

               -  Transmural myocardial infarction within 6 months prior to registration

               -  Acute bacterial or fungal infection requiring intravenous antibiotics at the time
                  of registration; Note: if the infection resolves and the patient is on oral
                  (p.o.) and still within, the required registration timeframe, then the patient is
                  eligible

               -  Chronic obstructive pulmonary disease exacerbation or other respiratory illness
                  requiring hospitalization or precluding study therapy at the time of registration

               -  Idiopathic pulmonary fibrosis or other severe interstitial lung disease that
                  requires oxygen therapy or is thought to require oxygen therapy within 1 year
                  prior to registration

               -  History of (non-infectious) pneumonitis that required steroids or current
                  pneumonitis

               -  Acquired immune deficiency syndrome (AIDS) based upon current Center for Disease
                  Control and Prevention (CDC) definition; note: human immunodeficiency 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 cisplatin and IMRT
                  involved in this protocol may be significantly immunosuppressive; patients with
                  known HIV, CD4 counts >= 250/uL, and undetectable viral loads who are stable on
                  an antiretroviral regimen may be included

               -  A diagnosis of immunodeficiency or is receiving systemic steroid therapy or any
                  other form of immunosuppressive therapy within 7 days prior to the first dose of
                  the MK-3475 (pembrolizumab)

               -  Known history of active TB (Bacillus tuberculosis)

               -  Known active hepatitis B (e.g., hepatitis B surface antigen [HBsAg] reactive) or
                  hepatitis C (e.g., hepatitis c virus [HCV] ribonucleic acid [RNA] [qualitative]
                  is detected); Note: patients who have been curatively treated for hepatitis C and
                  have no detectable viral load are eligible

               -  Active autoimmune disease that has required systemic treatment in the 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, etc.) is not considered a form of systemic treatment

          -  Grade 3-4 electrolyte abnormalities (CTCAE, v. 4):

          -  Serum calcium (ionized or adjusted for albumin) < 7 mg/dl (1.75 mmol/L) or > 12.5
             mg/dl (> 3.1 mmol/L) despite intervention to normalize levels

          -  Glucose < 40 mg/dl (< 2.2 mmol/L) or > 250 mg/dl (> 14mmol/L)

          -  Magnesium < 0.9 mg/dl (< 0.4 mmol/L) or > 3 mg/dl (> 1.23 mmol/L) despite intervention
             to normalize levels

          -  Potassium < 3.0 mmol/L or > 6 mmol/L despite intervention to normalize levels

          -  Sodium < 130 mmol/L or > 155 mmol/L despite intervention to normalize levels

          -  Patients who are pregnant, nursing, or expecting to conceive or father children within
             the projected duration of the trial, starting with the pre-screening or screening
             visit through 120 days after the last dose of MK-3475 (pembrolizumab)

          -  Hypersensitivity to MK-3475 (pembrolizumab) or any of its excipients;

          -  Patients who have received a live vaccine within 30 days of planned start of study
             therapy; Note: seasonal influenza vaccines for injection are generally inactivated flu
             vaccines and are allowed; however intranasal influenza vaccines (e.g., Flu-Mist) are
             live attenuated vaccines, and are not allowed

          -  Patients for whom it is not in the best interest to participate in the study, in the
             opinion of the treating investigator