This is a pilot study in pediatric and young adult patients with chronic phase CML (CML-CP) who are currently being treated with a tyrosine kinase inhibitor (TKI). Treatment with a TKI is currently life long. Pediatric patients with CML have long life spans, therefore they will be taking a TKI for a long time, especially during periods of growth and development, and therefore are believed to be at a significantly increased risk for side effects. Patients in this study will stop taking TKI medication and be closely monitored for 3 years to see if they remain cancer free. If their CML returns,...