Ponatinib Hydrochloride as Second Line Therapy in Treating Patients With Chronic Myeloid Leukemia in Chronic Phase Resistant or Intolerant to Imatinib Mesylate, Dasatinib, or Nilotinib

Inclusion Criteria: * Diagnosis of Philadelphia chromosome (Ph)-positive (by cytogenetics or fluorescent in situ hybridization \[FISH\]) or breakpoint cluster region (BCR)-ABL-positive (by polymerase chain reaction \[PCR\]) CML in chronic phase. * Participants should have demonstrated to have failure to therapy to one FDA-approved second-generation TKI (currently bosutinib, dasatinib, and nilotinib are approved as frontline therapy), defined as per European leukemiaNet (ELN)35 or National Comprehensive Cancer Network (NCCN) recommendations: * Less than complete hematologic response (CHR) at or beyond 3 months * No partial cytogenetic response at or beyond 3 months * BCR-ABL1 ≥ 10% at or beyond 3 months * BCR-ABL1 ≥ 1% at or beyond 6 months * Loss of CCyR or development of mutations or other clonal chromosomal abnormalities at any time during TKI treatment * Age \>18 years * ECOG performance of 0-2. * Adequate end organ function, defined as the following: total bilirubin ≤1.5x ULN (unless due to Gilbert syndrome, in which case it should be ≤3.0x ULN), SGPT ≤2.5x ULN, creatinine clearance (CrCL) ≥ 30 mL/min (Cockcroft-Gault formula). * Participants must sign an informed consent indicating they are aware of the investigational nature of this study, in keeping with the policies of the hospital. * Women of pregnancy potential must practice an effective method of birth control during the course of the study, in a manner such that risk of failure is minimized: * Prior to study enrollment, women of childbearing potential (WOCBP) must be advised of the importance of avoiding pregnancy during trial participation and the potential risk factors for an unintentional pregnancy. * Postmenopausal women must be amenorrheic for at least 12 months to be considered of non-childbearing potential OR women who are surgically sterile. * In addition, men enrolled on this study should understand the risks to any sexual partner of childbearing potential and should practice an effective method of birth control. * Women and men must continue birth control for the duration of the trial and at least 3 months after the last dose of study drug. * All WOCBP MUST have a negative pregnancy test prior to first receiving investigational product. * Participants should have discontinued therapy with bosutinib, dasatinib or nilotinib or other anti-leukemia therapy (except hydroxyurea), at least 48 hours prior to start of study therapy and recovered from any toxicity due to these therapies to at least grade 1. The use of hydroxyurea is allowed immediately prior to study entry. Exclusion Criteria: * Prior therapy with other BCR-ABL-targeted TKIs except bosutinib, dasatinib or nilotinib. Participants with T315I mutations are eligible and will be analyzed separately. * Active NYHA cardiac class 3-4 heart disease * Have clinically significant, uncontrolled, or active cardiovascular disease, specifically including, but not restricted to: * Any history of MI, unstable angina, cerebrovascular accident, or TIA * Any history of peripheral vascular infarction, including visceral infarction * Any revascularization procedure, including the placement of a stent * Congestive heart failure (CHF) (New York Heart Association \[NYHA\] class III or IV) within 6 months prior to enrollment, or left ventricular ejection fraction (LVEF) less than lower limit of normal, per local institutional standards, within 6 months prior to enrollment * History of clinically significant (as determined by the treating physician) atrial arrhythmia or any history of ventricular arrhythmia * Venous thromboembolism, including deep venous thrombosis or pulmonary embolism, within 6 months prior to enrollment * Participants with active, uncontrolled psychiatric disorders including: psychosis, major depression, and bipolar disorders. * Have uncontrolled hypertension (i.e., \>150 and \>90 for SBP and DBP, respectively). Participants with hypertension should be under treatment at study entry to ensure blood pressure control. Those requiring 3 or more antihypertensive medications should be discussed with the PI. * Have poorly controlled diabetes defined as HbA1c values of \> 7.5%. Participants with preexisting, well-controlled, diabetes are not excluded. * Pregnant or breast-feeding women are excluded. * Participants with history of pancreatitis within 1 year of study or history of chronic pancreatitis. * Participants in accelerated or blast phase, or patients who have ever been documented to be in blast phase CML, are excluded. The definitions of excluded CML phases are as follows: 1. Blastic phase: presence of 30% blasts or more in the peripheral blood or bone marrow. 2. Accelerated phase CML: presence of any of the following features: * Peripheral or marrow blasts 15% or more * Peripheral or marrow basophils 20% or more * Thrombocytopenia \< 100 x 109/L unrelated to therapy * Documented extramedullary blastic disease outside liver or spleen 3. Clonal evolution defined as the presence of additional chromosomal abnormalities other than the Ph chromosome has been historically been included as a criterion for accelerated phase. However, participants with clonal evolution as the only criterion of accelerated phase have a significantly better prognosis. Thus, participants with clonal evolution and no other criteria for accelerated phase will be eligible for this study, but analyzed separately. * Participants who have received more than one FDA-approved TKI for CML, or any investigational, non-FDA approved TKI.