This phase III ALCHEMIST treatment trial studies how well nivolumab after surgery and chemotherapy work in treating patients with stage IB-IIIA non-small cell lung cancer. Immunotherapy with monoclonal antibodies, such as nivolumab, may help the body's immune system attack the cancer, and may interfere with the ability of tumor cells to grow and spread.

PRIMARY OBJECTIVES: I. To evaluate whether adjuvant therapy with nivolumab will result in improved disease-free survival (DFS) over standard observation in patients with stage IB \>= 4 cm, II and IIIA, non-small cell lung cancer (NSCLC) following surgical resection and standard adjuvant therapy. II. To evaluate whether adjuvant therapy with nivolumab will result in improved disease-free survival (DFS) over standard observation in patients with stage IB \>= 4cm, II and IIIA, NSCLC with high PD-L1 expression (\>= 50% staining) following surgical resection and standard adjuvant therapy. III. To evaluate whether adjuvant therapy with nivolumab will result in improved overall survival (OS) over standard observation in patients with stage IB \>= 4cm, II and IIIA, NSCLC following surgical resection and standard adjuvant therapy. SECONDARY OBJECTIVES: I. To evaluate the safety profile of nivolumab when given as an adjuvant therapy. II. To evaluate and compare disease free and overall survival in patients with tumors that express PD-L1 in various patterns associated with nivolumab and standard observation. III. To evaluate and compare disease free and overall survival in patients with tumors that have high mutational load associated with nivolumab and standard observation. IV. To evaluate OS and DFS by stage. V. To evaluate OS and DFS by each stratification factor. OUTLINE: Patients are randomized to 1 of 2 arms. ARM I: Patients receive nivolumab intravenously (IV) over 30 minutes on day 1 of each cycle. Cycles repeat every 4 weeks for up to 1 year in the absence of disease progression or unacceptable toxicity. Patients also undergo computed tomography (CT) and/or positron emission tomography (PET)/CT throughout the trial and blood sample collection during screening and follow-up. Patients may undergo an echocardiography (ECHO) as clinically indicated on study. ARM II: Patients are followed serially with CT and/or PET/CT imaging for up to 1 year and then during follow-up. Patients also undergo blood sample collection during screening and follow-up. Patients may undergo an ECHO as clinically indicated on study. After completion of study treatment, patients are followed up at 6 weeks, every 3 months for 2 years, every 6 months for 2 years, and then every 12 months for 6 years.