This randomized phase III trial studies how well crizotinib works in treating patients with stage IB-IIIA non-small cell lung cancer that has been removed by surgery and has a mutation in a protein called anaplastic lymphoma kinase (ALK). Mutations, or changes, in ALK can make it very active and important for tumor cell growth and progression. Crizotinib may stop the growth of tumor cells by blocking the ALK protein from working. Crizotinib may be an effective treatment for patients with non-small cell lung cancer and an ALK fusion mutation.

PRIMARY OBJECTIVES: I. To evaluate whether adjuvant therapy with crizotinib will result in improved overall survival (OS) for patients with stage IB \>= 4 cm, II and IIIA, ALK-positive non-small cell lung cancer (NSCLC) following surgical resection. SECONDARY OBJECTIVES: I. To evaluate and compare disease-free survival (DFS) associated with crizotinib. II. To evaluate the safety profile of crizotinib when given in the adjuvant therapy setting. III. To collect tumor tissue and blood specimens for future research. OUTLINE: Patients are randomized to 1 of 2 treatment arms. ARM A: Patients receive crizotinib orally (PO) twice daily (BID) on days 1-21. Treatment repeats every 21 days for up to 2 years in the absence of disease progression or unacceptable toxicity. ARM B: Patients undergo observation. After completion of study treatment, patients are followed up every 6 months if \< 4 or 5 years from study entry, and every 12 months if 5-10 or 6-10 years from study entry.