Radiation and Chemotherapy With Ipilimumab Followed by Nivolumab for Patients With Stage III Unresectable Non-Small Cell Lung Cancer (NSCLC)

Inclusion Criteria: * Over 18 years of age * Participants must have signed and dated a written informed consent form. * Participants must be willing and able to comply with proposed visit and treatment schedule. * Patients with NSCLC documented by histology or cytology from brushing, washing, or needle aspiration of a defined lesion, but not from sputum cytology alone. * Patients must have presented at initial diagnosis with Stage III disease according to American Joint Committee on Cancer (AJCC) Staging Manual, 8th Edition; * Patients must be deemed by the treating investigator to be surgically unresectable. I * Eastern Cooperative Oncology Group (ECOG) Performance Status (PS) 0 or 1 * Patients must initiate study treatment 60 days from the date of pathologic diagnosis. * Tumor biopsy specimen including at least formalin-fixed, paraffin-embedded (FFPE) tumor tissue block or 10 unstained slides of tumor sample (archival or recent) for biomarker evaluation must be available for submission to the central lab for correlative studies. * Women of childbearing potential (WOCBP) must have a negative serum or urine pregnancy test within 14 days prior to the start of thoracic radiation therapy. * Male participants must be willing to refrain from sperm donation during the entire study and for 5 half-lives of study drug plus 90 days (duration of sperm turnover). * Investigators shall counsel WOCBP and male participants who are sexually active with WOCBP on the importance of pregnancy prevention and the implications of an unexpected pregnancy. Investigators shall advise on the use of highly effective methods of contraception which have a failure rate of \</= 1% when used consistently and correctly. Azoospermic males are exempt from contraceptive requirements. * WOCBP must agree to follow instructions for method(s) of contraception for the duration of treatment with study drug(s) plus 5 half-lives of study drug (half-life up to 25 days) plus 30 days (duration of ovulatory cycle) for a total of 5 months post-treatment completion. * WOCBP who are continuously not heterosexually active are exempt from contraception requirements. However, they must still undergo pregnancy testing as described in this section. * Males who are sexually active with WOCBP must agree to follow instructions for method(s) of contraception for the duration of treatment with study drug (s) plus 5 half-lives of the study drug (half-life up to 25 days) plus 90 days (duration of sperm turnover) for a total of 7 months post-treatment completion Exclusion Criteria: * All toxicities attributed to prior anti-cancer therapy must have been resolved to Grade 1 (NCI CTCAE Version 4) or baseline before administration of study drug(s). Exceptions may apply. * Women who are pregnant or breastfeeding * Active, known, or suspected autoimmune disease. Patients with an autoimmune paraneoplastic syndrome requiring concurrent immunosuppressive treatment are excluded. Patients with type I diabetes mellitus, hypothyroidism only requiring hormone replacement, skin disorders (such as vitiligo, psoriasis, or alopecia) not requiring systemic treatment, or conditions not expected to recur in the absence of an external trigger are permitted to enroll * A condition requiring systemic treatment with either corticosteroids (\> 10 mg daily prednisone equivalent) or other immunosuppressive medications within 14 days of study initiation. Corticosteroids with minimal systemic absorption (inhaled or topical steroids) and adrenal replacement steroid doses \> 10 mg daily prednisone equivalent are permitted in the absence of active autoimmune disease * Prior therapy with anti-PD-1, anti-PD-L1, anti-PD-L2, anti-CD137, or anti-CTLA-4 antibody * Interstitial lung disease that is symptomatic or may interfere with the detection or management of suspected drug-related pulmonary toxicity. * Any patient requiring supplemental oxygen therapy. * Previous malignancies (except non-melanoma skin cancers, and some in situ cancers) unless a complete remission was achieved at least 2 years prior to study entry AND no additional therapy is required during the study period. * Known medical condition that, in the investigator's opinion, would increase the risk associated with study participation or study drug(s) administration or interfere with the interpretation of safety results * Major surgery or significant traumatic injury that is not recovered at least 14 days before the initiation of thoracic radiation therapy. * Positive test for hepatitis B virus (HBV) using HBV surface antigen (HBVsAg) test or positive test for hepatitis C virus (HCV) using HCV ribonucleic acid (RNA) or HCV antibody test indicating acute or chronic infection. Individuals with a positive test for HCV antibody but no detection of HCV RNA indicating no current infection are eligible. * Known medical history of testing positive for human immunodeficiency virus (HIV) or known medical history of acquired immunodeficiency syndrome (AIDS) * Inadequate hematologic function. * Inadequate hepatic function. * Inadequate pancreatic function. * History of allergy or hypersensitivity to any of the study drugs or study drug components