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

The drug being tested in this study is ponatinib. This study will characterize the safety and efficacy of ponatinib over a range of 3 starting doses. The study will enroll 276 participants in 3 cohorts and each cohort will have 92 participants. All the participants will be randomized to receive once-daily oral administration of 1 of 3 starting doses of ponatinib: * Cohort A: 45 mg ponatinib tablet * Cohort B: 30 mg ponatinib tablet * Cohort C: 15 mg ponatinib tablet The study is designed to consist of 2 periods: 24-cycle Main treatment period and optional treatment continuation period. Participants will be treated with their randomized dose of study drug in the Main Treatment Period until the occurrence of at least one of the following: absence of CHR by 3 months, absence of MCyR at 12 months, absence of \<=1% BCR-ABL1IS at 12 months, loss of \<=1% BCR-ABL1IS development of intolerance, or completion of all 24 cycles of treatment (whichever occurs first). Following completion of approximately 5 years or following early withdrawal, participants may enter into an optional treatment continuation period. This multi-center trial will be conducted in the United States, United Kingdom, Republic of Korea, Spain, France, Taiwan, Australia, Canada, Italy, Chile, Japan, Germany, Argentina, Poland, Czech Republic, Denmark, Hong Kong, Portugal, Russia, Singapore, Switzerland, and Sweden. The overall time to participate in this study is approximately 96 months. Participants will make a final visit to the clinic approximately 30 days after the last dose of study treatment.