For more information regarding BMS clinical trial participation, please visit www.BMSStudyConnect.com. Inclusion Criteria: - Chronic Phase (CP)-CML Ph+ patients with complete hematologic response (CHR) but without one log BCR-ABL reduction (BCR-ABL level >10% IS) 3 months of imatinib 400mg treatment. (Imatinib transient dose adjustments due to Adverse Event (AEs) are allowed with a maximum of 2 weeks interruption of treatment with imatinib (cumulative) within the 3 month period before randomization). Imatinib monotherapy must have been started within 6 months of CP-CML diagnosis (Ph + /BCR-ABL detection) - Currently tolerating imatinib 400mg QD. Patients with prior imatinib treatment interruption or dose reductions are required to be on treatment with 400 mg imatinib for two weeks immediately prior to randomization to ensure tolerance to imatinib - Eastern Co-Operative Group (ECOG) performance status = 0 - 2 - Adequate renal function defined as serum creatinine ≤3 times the institutional upper limit of normal (ULN) - Adequate hepatic function defined as: total bilirubin ≤2.0 times the institutional ULN; alanine aminotransferase (ALT) and aspartate aminotransferase (AST) ≤2.5 times the institutional ULN Exclusion Criteria: - Previous diagnosis of accelerated phase or blast crisis - Subjects with clonal evolution in Ph+ cells observed in ≥2 metaphases at baseline bone marrow cytogenetic test, unless the same abnormalities were present at diagnosis. Patients with no evidence of clonal evolution, including those patients whose cytogenetic testing fails or bone marrow aspiration is a dry tap at 3 months, are eligible for the study - Subjects with less than CHR after 3 months of imatinib treatment or lost CHR after initial achievement - Documented T315I/A, F317L, or V299L mutations (if already available - not required for screening) - A serious uncontrolled medical disorder or active infection that would impair the ability of the subject to receive protocol therapy