Study of Immune Checkpoint Inhibition With Radiation Therapy in Unresectable, Non-metastatic Pancreatic Cancer

Inclusion: * Histopathological confirmation of pancreatic adenocarcinoma prior to study entry. * Unresectable and non-metastatic disease * At least 1 measurable metastatic lesion by RECIST 1.1, defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded) as \>20 mm with conventional techniques, or as \>10 mm with spiral computed tomography (CT) scan, and that is accessible for biopsy. * Age \>18 years * ECOG performance status 0-1 * Normal organ and marrow function as defined below: Absolute Neutrophil Count \> 1,000/mcL Platelets ≥ 75,000/mcL Total Bilirubin ≤ 2 x ULN Serum Albumin ≥ 2.5 g/dl ALT or AST up to 3 x ULN if no liver metastases or ALT or AST up to 5 x ULN if liver metastases present Creatinine \< 2 x institution upper limit of normal OR Creatinine Clearance \> 45 mL/min/1.73 m2, as calculated below, for patients with creatinine levels above institutional normal * No history of another malignancy in the past 5 years, except for treated non-melanoma skin cancer, superficial bladder cancer, or carcinoma-in-situ of the cervix * No coexisting medical problems that would limit compliance with the study * Ability to understand and sign a written informed consent document. Patient must have willingness and ability to comply with scheduled visits, treatment plans, laboratory tests and other study procedures. * Female subjects of childbearing potential must have a negative serum pregnancy test prior to study entry * Female subjects of childbearing potential and males must agree to use a highly effective method of contraception for the duration of study treatment, and for six months after discontinuation of the study drug. Exclusion: * Resectable, borderline resectable or metastatic disease * Prior chemotherapy, targeted therapy, immunotherapy, clinical trials or radiotherapy for pancreatic cancer. * Active or history of concomitant therapy with any of the following: interleukin (IL) 2, interferon, or other non-study immunotherapy regimens, immunosuppressive agents, other investigational therapies, or chronic use of systemic corticosteroids (inhaled and topical steroids are permitted) * Active or history of chronic autoimmune disease with symptomatic disease within the 3 years before randomization. * Active or history of inflammatory bowel disease (colitis, Crohn's disease), irritable bowel disease, celiac disease, or other serious, chronic, gastrointestinal conditions associated with diarrhea. * Diverticulitis within the past 2 years. * Active HIV infection * Uncontrolled systemic disease including, but not limited to, ongoing or active systemic infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements. * Brain metastases * Patients should not be vaccinated with live attenuated vaccines within 1 month of starting tremelimumab and MEDI4736 treatment. * History of hypersensitivity reaction to human or mouse antibody products * Evidence of pre-existing idiopathic pulmonary fibrosis on CT scan at baseline * Unhealed surgical wound at time of treatment, or history of unhealed surgical wound for more than 30 days * History of an invasive secondary primary malignancy diagnosed within the previous 3 years, except for appropriately treated stage I endometrial or cervical carcinoma, prostate carcinoma treated surgically or non-melanoma skin cancer. * Non-protocol antineoplastic agents will not be permitted during this study * Patients may not recieve other investigational agents. * Pregnant or lactating women * Subjects with dementia or significantly altered mental status that would prohibit understanding or rendering of information and consent and compliance with the requirements of the protocol. * Subjects unable or unwilling to abide by the study protocol or cooperate fully.