Pembrolizumab + Radiation for Locally Adv SCC of the Head and Neck (SCCHN) Not Eligible Cisplatin

Inclusion Criteria:

* Be willing and able to provide written informed consent/assent for the trial
* Be greater than or equal to 18 years of age
* Eastern Cooperative Oncology Group (ECOG) Performance Status less than or equal to 1
* Histologically or cytologically confirmed stage III-IV (non-metastatic) squamous cell carcinoma of the head and neck as defined by American Joint Committee on Cancer. Nasopharyngeal cancer patients will be excluded.
* Ineligible for high dose cisplatin therapy; the reason for ineligibility must be defined.
* Demonstrate adequate organ function. All screening labs should be performed within 14 days of treatment initiation.
* No prior curative attempts for this cancer (i.e., surgery, radiation and/or other).
* Female patients of childbearing potential should have a negative urine or serum pregnancy within 72 hours prior to receiving the first dose of study medication. Serum pregnancy test may be required.
* Female patients of childbearing potential should be willing to use 2 methods of birth control or be surgically sterile, or abstain from heterosexual activity for the course of the study through 120 days after the last dose of study medication.
* Male patients should agree to use an adequate method of contraception starting with the first dose of study therapy through 120 days after the last dose of study therapy.
* As determined by the enrolling physician or protocol designee, ability of the patient to understand and comply with study procedures for the entire length of the study.
* Consent for the use of any residual material from biopsy (archival tissue) and serial blood draws will be required for enrollment.

Exclusion Criteria:

* If currently participating in or has participated in a study of an investigational agent or using an investigational device within 4 weeks of the first dose of treatment.
* Has 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 trial treatment.
* Has had a prior monoclonal antibody within 4 weeks prior to study Day 1 or who has not recovered from adverse events due to agents administered more than 4 weeks earlier
* Had prior chemotherapy, targeted small molecule therapy, or radiation therapy within 2 weeks prior to study Day 1 or who has not recovered from adverse events due to a previously administered agent.
* Has a known additional malignancy that is metastatic, progressing or requires active treatment.
* Has an active autoimmune disease requiring systemic treatment within the past 3 months or a documented history of clinically severe autoimmune disease even if resolved; patients with vitiligo or resolved childhood asthma/atopy would be an exception to this rule.
* Has clinical or radiologic evidence of interstitial lung disease or active, non-infectious pneumonitis
* Has an active infection requiring systemic therapy.
* Has a history or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the trial, interfere with the patient's participation for the full duration of the trial, or is not in the best interest of the patient to participate, in the opinion of the treating investigator.
* Has known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial.
* Has inadequate home environment or social support to safely complete the trial procedures.
* 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-programmed cell death (PD-1), anti-PD-L1, anti-PD-L1, anti-CD137, or anti-Cytotoxic T-lymphocyte-associated antigen-4 (CTLA-4) antibody.
* Has a known history of Human Immunodeficiency Virus (HIV) HIV 1/2 antibodies) Has 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 prior to the first dose of trial treatment.
* Has a history of (non-infectious) pneumonitis that required steroids or current pneumonitis