Crizotinib in Treating Patients With Stage IB-IIIA Non-small Cell Lung Cancer That Has Been Removed by Surgery and ALK Fusion Mutations (An ALCHEMIST Treatment Trial)

Inclusion Criteria: * Patients must have undergone complete surgical resection of their stage IB (\>= 4 cm), II, or non-squamous IIIA NSCLC per American Joint Committee on Cancer (AJCC) 7th edition and have had negative margins; N3 disease is not allowed * Baseline chest computed tomography (CT) with or without contrast must be performed within 6 months (180 days) prior to randomization to ensure no evidence of disease; if clinically indicated additional imaging studies must be performed to rule out metastatic disease * Eastern Cooperative Oncology Group (ECOG) performance status 0 or 1 * Patients must be registered to the ALCHEMIST-SCREEN (ALLIANCE A151216) trial prior to randomization * Positive for translocation or inversion events involving the ALK gene locus (e.g. resulting in echinoderm microtubule associated protein like 4 \[EML4\]-ALK fusion) as determined by the Vysis Break Point fluorescence in situ hybridization (FISH) assay and defined by an increase in the distance between 5? and 3? ALK probes or the loss of the 5? probe; this must have been performed: * By a local Clinical Laboratory Improvement Amendments (CLIA) certified laboratory: report must indicate the results as well as the CLIA number of the laboratory which performed the assay; tissue must be available for submission for central, retrospective confirmation of the ALK fusion status via ALCHEMIST-SCREEN (ALLIANCE A151216) OR * Patient registered to and the ALK fusion status performed centrally on t…