This phase III trial studies how well an antibody (durvalumab) with chemotherapy and radiation therapy (chemoradiation) works in treating patients with stage III non-small cell lung cancer that cannot be removed by surgery (unresectable). Immunotherapy with monoclonal antibodies, such as durvalumab, may help the body’s immune system attack the cancer, and may interfere with the ability of tumor cells to grow and spread. This study is being done to see if adding durvalumab to standard chemoradiation followed by additional durvalumab can extend patients life and / or prevent the tumor from coming back compared to the usual approach of chemoradiation alone followed by durvalumab. Eligibility includes being at least 18 years old, newly diagnosed stage IIIA/B/C non-small cell lung cancer (NSCLC) (per the American Joint Committee on Cancer [AJCC] 8th edition) that is unresectable and is histologically and/or cytologically confirmed * Nodal recurrence after surgery for early stage NSCLC, patient must have an Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1, body weight > 30 kg of patients. Additional eligibility requirements are necessary and can be reviewed with a clinical trials coordinator upon request.