Durvalumab and Consolidation SBRT Following Chemoradiation for Locally Advanced Stage III Non-Small Cell Lung

Inclusion Criteria: * Stage III NSCLC. * Completion of concurrent chemoradiation: • Radiation dose of 60.0 Gy (50-65Gy) using standard fractionation * Patients will receive the first dose of durvalumab \> 3 weeks and \< 7 weeks after their last treatment of chemoradiation (last radiation or chemotherapy treatment, whichever ended last).Sites are required to submit prior treatment (chemotherapy and radiation) * Residual tumor volume that is appropriate for SBRT • Residual Primary tumor \<120cc (approximately 6cm diameter). * Absolute neutrophil count ≥ 1,000/uL, platelet ≥ 60,000/uL prior to registration. * Total bilirubin ≤ 1.5x upper institutional limit of normal (ULN), and AST and ALT ≤ 3x ULN. * ECOG performance status 0 to 1 * Minimum life expectancy of 12 weeks as determined by treating physician. * Age \> 18 years. * Voluntary, signed written informed consent. * Women of childbearing potential must have a negative serum pregnancy test within 7 days of day 1 of treatment (post-menopausal women, defined as surgical menopause or lack or menses \>12 months, do not need to have a pregnancy test, document status.) * Men and women of childbearing potential must be willing to consent to using effective contraception while on treatment and for at least 6 months after the last treatment. * Resolution of all related toxicities from chemo/RT to \< grade 2, except alopecia. * Patient must have tissue available from prior biopsy for correlative studies as confirmed by treating physician. Exclusion Criteria: * Disease progression during or after standard chemoradiation * Prior thoracic radiation (other than the chemoradiation delivered prior to SBRT) * Metastatic disease * Uncontrolled severe, intercurrent illness as confirmed by the treating physician. * Chemotherapy within 3 weeks from the first treatment on study (day 1). * Prior complete resection of all NSCLC (patients could have undergone prior resection as long as it is not complete and the patient meets criteria and staging and tumor volume for registration). * Severe, active co-morbidity, defined as follows: * Uncontrolled neuropathy ≥ grade 2 regardless of cause; * Unstable angina and/or congestive heart failure requiring hospitalization within the last 6 months; * Transmural myocardial infarction within the last 6 months; * Acute bacterial or fungal infection requiring intravenous antibiotics at the time of registration; * Severe hepatic disease, defined as a diagnosis of Child-Pugh Class B or C hepatic disease. * HIV positive with CD4 count \< 200 cells/microliter. Note that patients who are HIV positive are eligible, provided they are under treatment with highly active antiretroviral therapy (HAART) and have a CD4 count ≥ 200 cells/microliter within 30 days prior to registration. Note also that HIV testing is not required for eligibility for this protocol unless patient is known to be HIV positive and they do not had a CD4 count result within 30 days prior to registration. * 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, not inclusive of patients who are HIV positive and who meet criterion above. Note: Patients who require continuous or intermittent steroid therapy for non-autoimmune conditions, e.g. asthma, osteoarthritis or intravenous contrast allergy, are eligible permitted those patients who receive continuous steroids are limited to a dose of ≤10 mg/day of prednisone (or equivalent). Higher doses are permitted for intermittent therapy, e.g. for contrast allergy, but will need to be approved by BrUOG prior to registration. * Has a known history of active tuberculosis * Hypersensitivity to Durvalumab or any of its excipients * Has 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 (e.g., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency, etc.) is not considered a form of systemic treatment * Has known history of clinically significant pneumonitis * Has an active infection requiring intravenous systemic therapy at the time of registration * 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 treating physician * Has known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial as per the treating physician * Is pregnant or breastfeeding * Has received prior therapy with an anti-CTLA-4, -PD-1, -PD-L1, or -PD-L2 agent * Has a known active Hepatitis B (e.g., HBsAg reactive) or Hepatitis C (e.g., HCV RNA)