Unresectable Stage IIIA/IIIB Non-small Cell Lung Cancer (NSCLC)

Inclusion Criteria: Subject must meet all of the following applicable inclusion criteria to participate in this study: * Written informed consent and HIPAA authorization for release of personal health information. * Age ≥ 18 years at the time of consent. * ECOG Performance Status of 0 or 1 within 14 days prior to registration. * Histological or cytological confirmation of NSCLC. A pathology report confirming the diagnosis of NSCLC must be obtained and reviewed by the treating physician prior to registration to study. * Must have unresectable or inoperable stage IIIA or IIIB disease according to the 7th edition IASLC stage classification for lung cancer. Subjects must be considered unresectable or inoperable based on the judgment of the treating physician. * Subjects must have completed concurrent chemoradiation with a platinum doublet and a dose of radiation ranging from 59.4-66.6 Gy. Subjects must have stable disease or disease response as evidenced on CT or PET scan evaluation. For those eligible, protocol therapy should begin within 56 days of completing chemoradiation OR Subjects must have completed up to 2 cycles of consolidation therapy started within 56 days of completion of radiation. After completion of consolidation chemotherapy, subjects must have stable disease or disease response as evidenced by CT or PET scan evaluation. For those eligible, protocol therapy should begin within 56 days after the last cycle of chemotherapy. * Prior cancer treatment must be completed between 1-56 days prior to registration and the subject must have recovered from all reversible acute toxic effects of the regimen (other than alopecia) to ≤Grade 1 or baseline. * Demonstrate adequate organ function, all screening labs to be obtained within 14 days prior to registration: Hematological: * Absolute Neutrophil Count (ANC) ≥ 1.5 K/mm\^3 * Hemoglobin (Hgb) ≥ 9 g/dL * Platelets ≥100,000/mcl Renal: * Serum creatinine OR Measured or calculated creatinine clearance (GFR can also be used in place of creatinine or CrCl) ≤ 1.5 x upper limit of normal (ULN) OR ≥ 60 mL/min for subjects with creatinine levels \>1.5 x institutional ULN Hepatic: * Bilirubin ≤ 1.5 × ULN OR Direct bilirubin of ≤ ULN for subjects with total bilirubin levels of \>1.5x ULN * Aspartate aminotransferase (AST) ≤ 2.5 × ULN * Alanine aminotransferase (ALT) ≤ 2.5 × ULN Coagulation: * International Normalized Ratio (INR) or Prothrombin Time (PT) Activated Partial Thromboplastin Time (aPTT) ≤1.5 X ULN unless subject is receiving anticoagulant therapy as long as PT/INR/PTT is within therapeutic range of intended use of anticoagulants * Women of childbearing potential (WOCBP) must have a negative serum or urine pregnancy test (minimum sensitivity 25 IU/L or equivalent units of HCG) within 7 days prior to registration. NOTE: Women are considered of childbearing potential unless they are surgically sterile (have undergone a hysterectomy, bilateral tubal ligation, or bilateral oophorectomy) or are post-menopausal. Menopause is defined clinically as 12 months of amenorrhea in a woman over 45 in the absence of other biological or physiological causes. In addition, women under the age of 62 must have a documented serum follicle stimulating hormone (FSH) level less than 40 mIU/mL to be considered post-menopausal. * Women of childbearing potential must be willing to abstain from heterosexual activity or use an effective method of contraception from the time of informed consent until 23 weeks after treatment discontinuation. * Men who are sexually active with women of childbearing potential (WOCBP) must use any contraceptive method with a failure rate of less than 1% per year. Men receiving study drug and who are sexually active with WOCBP will be instructed to adhere to contraception for a period of 31 weeks after the last dose of investigational product. * As determined by the enrolling physician or protocol designee, ability of the subject to understand and comply with study procedures for the entire length of the study. Exclusion Criteria: Subjects meeting any of the criteria below may not participate in the study: * 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 23 weeks (female) or 31 weeks (male) after the last dose of trial treatment. * Active central nervous system (CNS) metastases. Subjects must undergo a head computed tomography (CT) scan or brain MRI within 28 days prior to registration for protocol therapy to exclude brain metastases if symptomatic or without prior brain imaging. * Treatment with any investigational agent within 28 days prior to registration for protocol therapy. * Prior chemotherapy, adjuvant therapy, or radiotherapy for lung cancer other than standard concurrent chemoradiation or up to 2 cycles of consolidation. * Prior therapy with a PD-1, PD-L1, PD-L2 or CTLA-4 inhibitor or a lung cancer-specific vaccine therapy. * Presence of metastatic disease (stage IV NSCLC) is not allowed. Subjects must be evaluated with a CT or PET scan prior to registration for protocol therapy to exclude metastatic disease. * Active second cancers. * Evidence of active autoimmune disease requiring systemic treatment within the past 90 days or a documented history of clinically severe autoimmune disease, or a syndrome that requires systemic steroids or immunosuppressive agents. Subjects with vitiligo or resolved childhood asthma/atopy would be an exception to this rule. Subjects that require intermittent use of bronchodilators or local steroid injections would not be excluded from the study. Subjects with hypothyroidism stable on hormone replacement or Sjogren's syndrome will not be excluded from the study. * Interstitial lung disease or history of pneumonitis requiring treatment with corticosteroids. * Diagnosis of immunodeficiency or is receiving chronic systemic corticosteroid therapy or other immunosuppressive therapy (excludes inhaled corticosteroids) within 7 days of first dose of study drug. * History of psychiatric illness or social situations that would limit compliance with study requirements. * Clinically active infection as judged by the site investigator (≥ Grade 2 by CTCAE v4). * History of human immunodeficiency virus (HIV) infection or chronic hepatitis B or C. * Has a 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. * Has a known history of active TB (Bacillus Tuberculosis). * Hypersensitivity to nivolumab, ipilimumab, or any of their excipients. * Has received a live vaccine within 30 days prior to planned start of study therapy. Note: 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.