The study will assess the role of high-dose imatinib mesylate, in patients who have taken imatinib mesylate for at least 1 year at the standard dose, in achieving a major molecular response (a measure of the level of chronic myelogenous leukemia) versus the standard dose.

Inclusion Criteria:

• Chronic myelogenous leukemia with Philadelphia chromosome
• 18 years and older
• Patients must have been taking imatinib mesylate standard dose for at least 12 months and have achieved a complete cytogenetic response but not a major molecular response.

Exclusion Criteria:

• Patients with cardiac problems such as congestive heart failure, or myocardial infarction within the last 6 months
• Patients with an uncontrolled medical disease such as uncontrolled diabetes, chronic renal (kidney) disease or active uncontrolled infection.
• Patients with other current primary malignancy or malignancy requiring active intervention

Other protocol defined inclusion/exclusion criteria may apply.