Chemoradiation vs Immunotherapy and Radiation for Head and Neck Cancer

Inclusion Criteria: * p16-positive squamous cell carcinoma of the pharynx, larynx or oral cavity * High-Intermediate Risk Disease, defined as: * T1-T3 N2 M0 or T3 N1 M0 or any stage III (T4 or N3) p16+ squamous cell carcinoma of the oropharynx (AJCC 8th edition staging system) * T1-2 N1-3 M0 or T3-4 N0-3 M0 (stage III-IVB) p16+ squamous cell carcinoma of the hypopharynx or larynx * T1-2 N2-3 M0 or T3-4 N0-3 M0 (stage III-IVB) p16+ squamous cell carcinoma of the nasopharynx * Inoperable T4 N0-3 M0 (stage IVA-IVB) p16+ squamous cell carcinoma of the oral cavity * Measurable disease based on RECIST 1.1 * Adequate hematologic function within 28 days prior to registration * Adequate renal and hepatic function * Female subject of childbearing potential should have a negative pregnancy test * Female subjects of childbearing potential must agree to use an adequate method of contraception for the course of the study * Male subjects must agree to use an adequate method of contraception for the course of the study Exclusion Criteria: * Prior malignancy within the past 3 years (except non-melanomatous skin cancer and early stage treated prostate cancer); * Prior head and neck radiation, chemotherapy, or immunotherapy; * Prior oncologic (radical) surgery to the primary site; * Documented evidence of distant metastases; * Severe, active co-morbidity defined as follows: * Unstable angina and/or congestive heart failure requiring hospitalization within the last 6 months; * Transmural 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 * Acquired Immune Deficiency Syndrome (AIDS) based upon current CDC definition; note, however, that HIV testing is not required for entry into this protocol. * Any medical or psychiatric illness, which, in the opinion of the principal investigator, would compromise the patient's ability to tolerate this treatment; * Psychiatric/social situations that would limit compliance with study requirements * Hypersensitivity to pembrolizumab or any of its excipients. * 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 (eg., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency, etc.) is not considered a form of systemic treatment. * Known history of, or any evidence of active, non-infectious pneumonitis. * Active infection requiring systemic therapy. * Is pregnant or breastfeeding, 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 trial treatment. * Has received prior therapy with an anti-PD-1, anti-PD-L1, or anti-PD-L2 agent. * Known history of Human Immunodeficiency Virus (HIV) (HIV 1/2 antibodies). * Known active Hepatitis B (e.g., HBsAg reactive) or Hepatitis C (e.g., HCV RNA \[qualitative\] is detected). * Has received a live vaccine within 30 days of planned start of study therapy.