Dasatinib and Venetoclax in Treating Patients With Philadelphia Chromosome Positive or BCR-ABL1 Positive Early Chronic Phase Chronic Myelogenous Leukemia

Inclusion Criteria: * Diagnosis of Ph-positive or BCR-ABL positive CML in early chronic phase CML (i.e., time from diagnosis ≤ 12 months). Except for hydroxyurea and/or 1 to 2 doses of cytarabine patients must have received no or minimal prior therapy, defined as \<1 month (30 days) of prior FDA approved TKI. * Clonal evolution defined as the presence of additional chromosomal abnormalities other than the Ph chromosome has historically been included as a criterion for accelerated phase. However, patients with clonal evolution as the only criterion of accelerated phase have a significantly better prognosis, and when present at diagnosis may not impact the prognosis at all. Thus, patients with clonal evolution and no other criteria for accelerated phase will be eligible for this study. * Eastern Cooperative Oncology Group (ECOG) performance of 0-2 * Total bilirubin \< 1.5 x upper limit normal (ULN) (unless secondary to Gilbert's disease, in which case should be \< 2.5x ULN) * Serum glutamate pyruvate transaminase (SGPT) \< 3 x ULN * Creatinine \< 1.5 x ULN * Patients must sign an informed consent indicating they are aware of the investigational nature of this study, in keeping with the policies of the hospital Exclusion Criteria: * New York Heart Association (NYHA) cardiac class 3-4 heart disease * Patients meeting the following criteria are not eligible unless cleared by cardiology: * Uncontrolled angina within 3 months * Diagnosed or suspected congenital long QT sy…