Adult patients age ≥18 years.

Patients must have a diagnosis of Ph-positive or BCR::ABL1 positive CML in chronic phase.

Patients who received prior hydroxyurea, 1 to 2 doses of cytarabine, and/or an FDA approved TKI for <30 days are eligible.

Patients with additional chromosomal abnormalities at diagnosis (early disease) and no other criteria for accelerated phase will be eligible for this study.

ECOG performance status ≤2.

Patients must have adequate end organ function, defined as the following: total bilirubin

≤1.5x ULN (unless secondary to Gilbert's disease, in which case should be ≤2.5x ULN), SGPT or SGOT ≤3x ULN, creatinine clearance ≥30mL/min calculated using modified Cockcroft-Gault.

Ability to understand and the willingness to sign a written informed consent document.

Dasatinib is known to be teratogenic. For this reason, women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation. (Refer to Pregnancy Assessment Policy MD Anderson Institutional Policy # CLN1114). This includes all female patients, between the onset of menses (as early as 8 years of age) and 55 years unless the patient presents with an applicable exclusionary factor which may be one of the following:

• Postmenopausal (no menses in greater than or equal to 12 consecutive months).
• History of hysterectomy or bilateral salpingo-oophorectomy.
• Ovarian failure (Follicle Stimulating Hormone and Estradiol in menopausal range, who have received Whole Pelvic Radiation Therapy).
• History of bilateral tubal ligation or another surgical sterilization procedure.

Approved methods of birth control are as follows: Hormonal contraception (i.e. birth control pills, injection, implant, transdermal patch, vaginal ring), Intrauterine device (IUD), Tubal Ligation or hysterectomy, Subject/Partner post vasectomy, Implantable or injectable contraceptives, and condoms plus spermicide. Not engaging in sexual activity for the total duration of the trial and the drug washout period is an acceptable practice; however periodic abstinence, the rhythm method, and the withdrawal method are not acceptable methods of birth control. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately.

For patients with evidence of chronic hepatitis B virus (HBV) infection, the HBV viral load must be undetectable on suppressive therapy, if indicated.

Patients with a history of hepatitis C virus (HCV) infection must have been treated and cured. For patients with HCV infection who are currently on treatment, they are eligible if they have an undetectable HCV viral load.

Human immunodeficiency virus (HIV)-infected patients on effective anti-retroviral therapy with undetectable viral load within 6 months are eligible for this trial.

Patients with a prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen are eligible for this trial.

Patients with known history or current symptoms of cardiac disease, or history of treatment with cardiotoxic agents, should have a clinical risk assessment of cardiac function using the New York Heart Association Functional Classification. To be eligible for this trial, patients should be class II or better.