Trial of Chemoradiation and Pembrolizumab in Patients With Rectal Cancer

Diagnosis/Condition for Entry into the Trial: * Histologically confirmed adenocarcinoma of the rectum * Clinical stage II (T3-4, N-) or stage III (any T, N+) rectal cancer based on pelvic MRI. * Tumor located within 12 cm of the anal verge (determined by rigid proctoscopy or flexible sigmoidoscopy). Subject Inclusion Criteria: * Be willing and able to provide written informed consent for the trial. * Be 18 years of age or older on day of signing informed consent. * Have measurable disease based on Response Evaluation Criteria in Solid Tumors 1.1 (RECIST 1.1). * Be willing to provide tissue from a newly obtained core or excisional biopsy of a tumor lesion. * Have a performance status of 0-1 on the Eastern Cooperative Oncology Group (ECOG) Performance Scale. * Female subject of childbearing potential should have a negative urine or serum pregnancy within 72 hours prior to receiving the first dose of study treatment. If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required. * Female subjects 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 treatment. Subjects of childbearing potential are those who have not been surgically sterilized or have not been free from menses for \> 1 year. * Male subjects 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 treatment. Subject Exclusion Criteria: * Unresectable disease, as evidenced by invading adjacent organs and surgical resection will not achieve negative margins * Recurrent rectal cancer * Evidence of metastatic disease (as determined by chest and abdominal CT). * Prior malignancy within the prior 5 years. Exceptions include basal cell carcinoma of the skin or squamous cell carcinoma of the skin that has undergone potentially curative therapy or in situ cervical cancer. * Prior radiation for other diagnoses to the expected rectal cancer treatment fields. * Prior surgery, radiation, chemotherapy, targeted therapy, or investigational therapy for rectal cancer. NOTE: If subject received major surgery for reason other than rectal cancer, they must have recovered adequately from the toxicity and/or complications from the intervention prior to starting therapy. * Prior therapy with an anti-PD-1, anti-PD-L1, or anti-PD-L2 agent. * Diagnosis of immunodeficiency or is receiving systemic steroid therapy or any other form of immunosuppressive therapy within 7 days prior to the planned start of study treatment. * 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). * Administration of live vaccine within 30 days of planned start of study therapy. 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. * Known history of active TB (Bacillus Tuberculosis) * 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. * History or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the trial, interfere with the subject's participation for the full duration of the trial, or is not in the best interest of the subject to participate, in the opinion of the site investigator. * Known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial. * Serious uncontrolled medical disorder that in the opinion of the site investigator would impair the ability of the subject to receive protocol therapy. * Unable or unwilling to participate a study related procedure, including MRI. * 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.