Purpose of this study is to compare any good and bad effects of using the study drug, crizotinib after completeion of surgery and in some cases after chemotherapy and/or radiation therapy for ALK-positive non-small cell lung cancer.

You will need to have the following extra exams and tests to find out if you can be in the research study:•Electrocardiogram (EKG) to check your heart rhythm•Blood or urine pregnancy test, if you are a woman of child-bearing potential•Smoking status survey•ALK Fusion Status test using tissue from your previous surgery and/or biopsiesToxicity assessment will be done every 3 weeks for the first 6 weeks, then every 6 weeks for the next 12 weeks, then every 12 weeks until treatment is completed.