Ponatinib in Participants With Resistant Chronic Phase Chronic Myeloid Leukemia (CP-CML) to Characterize the Efficacy and Safety of a Range of Doses

Inclusion Criteria:

1. Have chronic phase-chronic myelogenous leukemia/chronic myeloid leukemia (CP-CML) and have received at least two prior tyrosine kinase inhibitor (TKI) therapies and have demonstrated resistance to treatment OR have documented history of presence of T315I mutation after receiving any number of prior TKI.

   o\] The diagnosis of chronic myeloid leukemia (CML) will be made using standard hematopathologic and cytogenetic criteria; CP-CML will be defined by all of the following: i \<15% blasts in bone marrow ii \<30% blasts plus promyelocytes in bone marrow iii \<20% basophils in peripheral blood. iv \>= 100\*10\^9/liter (L) platelets (\>=100,000/mm\^3). v No evidence of extramedullary disease except hepatosplenomegaly vi No prior diagnosis of AP-CML, and BP-CML o\] Cytogenetic assessment at screening must demonstrate the BCR-ABL1 fusion by presence of the t(9;22) Philadelphia chromosome.

   i Variant translocations are only allowed provided they meet inclusion criterion 1d.

   o\] Resistance to prior TKI therapy is defined as follows (participants must meet at least 1 criterion): i Three months after the initiation of prior TKI therapy: No cytogenetic response (\>95% Ph+) or failure to achieve CHR or new mutation ii Six months after the initiation of prior TKI therapy: BCR-ABL1IS \>10% and/or Ph+ \>65% or new mutation iii Twelve months after the initiation of prior TKI therapy: BCR ABL1IS \>10% and/or Ph+ \>35% or new mutation iv At any time after the initiation of prior TKI therapy, the development of a new BCR-ABL1 kinase domain mutation(s) v At any time after the initiation of prior TKI therapy, the development of new clonal evolution vi At any time after the initiation of prior TKI therapy, the loss of CHR, or CCyR, or the confirmed loss of MMR in 2 consecutive tests, one of which has a BCR-ABL1IS transcript level of \>=1% or new mutation o\] \>1% of BCR-ABL1IS as shown by real-time polymerase chain reaction
2. Have an Eastern Cooperative Oncology Group (ECOG) performance status of 0, 1, or 2.
3. Have adequate renal function as defined by the following criterion:

   o\] Serum creatinine \<=1.5\*ULN for institution o\] Estimated creatinine clearance \>=30 milliliter per minute (mL/min) (Cockcroft-Gault formula)
4. Have adequate hepatic function as defined by the following criteria:

   o\] Total serum bilirubin \<=1.5\*ULN, unless due to Gilbert's syndrome o\] Alanine transaminase (ALT) \<=2.5\*ULN, or \<=5\*ULN if leukemic infiltration of the liver is present o\] Aspartate transaminase (AST) \<=2.5\*ULN, or \<=5\*ULN if leukemic infiltration of the liver is present
5. Have normal pancreatic status as defined by the following criterion:

   o\] Serum lipase and amylase \<=1.5\*ULN
6. Have normal QT interval corrected (Frederica) (QTcF) interval on screening electrocardiogram (ECG) evaluation, defined as QTcF of \<=450 milliseconds (ms) in males or \<=470 ms in females.
7. Have a negative pregnancy test documented prior to enrollment (for females of childbearing potential).
8. Agree to use a highly effective form of contraception with sexual partners from randomization through at least 4 months after the end of treatment (for female and male participants who are fertile).
9. Provide written informed consent.
10. Be willing and able to comply with scheduled visits and study procedures.
11. Have recovered from toxicities related to prior anticancer therapy to National Cancer Institute (NCI) Common Terminology Criteria for Adverse Events (CTCAE) v 4.0 grade \<=1.

Exclusion Criteria:

1. Have used any approved TKIs or investigational agents within 2 weeks or 6 half-lives of the agent, whichever is longer, prior to receiving study drug.
2. Received interferon, cytarabine, or immunotherapy within 14 days, or any other cytotoxic chemotherapy, radiotherapy, or investigational therapy within 28 days prior to receiving the first dose of ponatinib, or have not recovered (\>grade 1 by NCI CTCAE, version 4.0) from AEs (except alopecia), due to agents previously administered.
3. Have undergone autologous or allogeneic stem cell transplant \<60 days prior to receiving the first dose of ponatinib; have any evidence of ongoing graft-versus-host disease (GVHD) or GVHD requiring immunosuppressive therapy.
4. Are being considered for hematopoietic stem cell transplant (HSCT) within 6-12 months of enrollment (note: ponatinib is not to be used as a bridge to HSCT in this trial).
5. Are taking medications with a known risk of Torsades de Pointes.
6. Have previously been treated with ponatinib.
7. Have active CNS disease as evidenced by cytology or pathology; in the absence of clinical CNS disease, lumbar puncture is not required. History itself of CNS involvement is not exclusionary if CNS has been cleared with a documented negative lumbar puncture.
8. Have clinically significant, uncontrolled, or active cardiovascular disease, specifically including, but not restricted to:

   o\] Any history of myocardial infarction (MI), unstable angina, cerebrovascular accident, or Transient Ischemic Attack (TIA) o\] Any history of peripheral vascular infarction, including visceral infarction o\] Any revascularization procedure, including the placement of a stent o\] 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 o\] History of clinically significant (as determined by the treating physician) atrial arrhythmia or any history of ventricular arrhythmia o\] Venous thromboembolism, including deep venous thrombosis or pulmonary embolism, within 6 months prior to enrollment
9. Have uncontrolled hypertension (that is, \>150 and \>90 for systolic blood pressure (SBP) and diastolic blood pressure (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 medical monitor.
10. Have poorly controlled diabetes defined as HbA1c values of \>7.5%. Participants with preexisting, well-controlled diabetes are not excluded.
11. Have a significant bleeding disorder unrelated to CML.
12. Have a history of alcohol abuse.
13. Have a history of either acute pancreatitis within 1 year of study enrollment or of chronic pancreatitis.
14. Have malabsorption syndrome or other gastrointestinal illness that could affect oral absorption of study drug.
15. Have a history of another malignancy, other than cervical cancer in situ or basal cell or squamous cell carcinoma of the skin; the exception is if participants have been disease-free for at least 5 years, and are deemed by the investigator to be at low risk for recurrence of that malignancy.
16. Are pregnant or lactating.
17. Have undergone major surgery (with the exception of minor surgical procedures, such as catheter placement or BM biopsy) within 14 days prior to first dose of ponatinib.
18. Have an active infection which requires intravenous antibiotics.
19. Have a known history of human immunodeficiency virus infection; testing is not required in the absence of prior documentation or known history.
20. Have any condition or illness that, in the opinion of the investigator, would compromise participant safety or interfere with the evaluation of the drug.
21. Have hypersensitivity to the ponatinib active substance or to any of its inactive ingredients.