Inclusion Criteria 1. Cytogenetic or Polymerase Chain Reaction based diagnosis of Chronic phase of Philadelphia Chromosome Positive Chronic Myelogenous Leukemia (Part 1), any phase of Philadelphia Chromosome Positive Chronic Myelogenous Leukemia or Philadelphia Chromosome Positive Acute Lymphocytic Leukemia (Part 2), whose disease is resistant/refractory to full-dose imatinib (400 mg for chronic phase subjects/600 mg for advanced leukemia subjects), or are intolerant of any dose of imatinib. 2. Adequate duration of prior imatinib therapy. 3. No prior exposure to Src, Abl, or Src/Abl kinase inhibitors other than imatinib. 4. Eastern Cooperative Oncology Group Performance Status of 0 or 1 for chronic phase subjects, and 0, 1 or 2 for Advanced Stage subjects. 5. At least 7 days since any anti-proliferative treatment (including intrathecal chemotherapy) before the first dose of SKI-606, (except hydroxyurea). 6. Recovered to National Cancer Institute grade 0-1, or to baseline, from any toxicities of prior anti-tumor treatment, other than alopecia or thrombocytopenia due to active prior treatment (intolerant subjects). 7. At least 3 months post allogeneic stem cell transplantation before the first dose of SKI-606. 8. Able to take daily oral capsules reliably. 9. Absolute neutrophil count greater than 1,000/mL (Part 1) 10. Adequate hepatic, and renal function. 11. Documented normal INR if not on oral anticoagulant therapy, or, if on oral anticoagulant therapy consistent target INR less than 3. 12. Age should be greater than 20 years and less than 75 years (Part 1), greater than 20 years (Part 2), including women of childbearing potential. 13. Willingness of male and female subjects, who are not surgically sterile or postmenopausal, must agree and commit to the use of reliable methods of birth control (oral contraceptives, intrauterine devices, or barrier methods used with a spermicide) for the duration of the study and for 30 days after the last dose of SKI-606.

Exclusion Criteria

1. Subjects with Philadelphia chromosome negative Chronic Myelogenous Leukemia and Acute Lymphocytic Leukemia.
2. Overt leptomeningeal leukemia. Subjects must be free of CNS involvement according to the symptoms for a minimum of 2 months before the first dose of SKI-606. Subjects with CNS symptoms must have a diagnostic lumbar puncture prior to study enrollment. 3. Subjects with extramedullary disease only. 4. Ongoing requirement for warfarin or other oral anticoagulant therapy (Part 1). 5. Ongoing requirement for hydroxyurea (Part 1). 6. Graft Versus Host Disease. a. no previous Graft Versus Host Disease allowed (Part 1). b. no treated or untreated Graft Versus Host Disease within 60 days of first dose (Part 2). 7. Major surgery within 14 days or radiotherapy within 7 days before the first dose of SKI-606 (recovery from any previous surgery should be complete before day 1). 8. Ongoing clinical requirement for administration of a strong inhibitor or inducer of CYP-3A4 (Part 1). 9. History of clinically significant or uncontrolled cardiac disease including: a. history of a clinically significant ventricular arrhythmia (such as ventricular tachycardia, ventricular fibrillation, or Torsades de pointes) b. diagnosed or suspected congenital or acquired prolonged QT syndrome c. history of prolonged QTc d. unexplained syncope e. history of or active congestive heart failure f. myocardial infarction within 12 months. g. Uncontrolled angina or hypertension within 3 months 10. Baseline QTcF greater than 0.45 sec (average of triplicate readings) 11. Concomitant use of or need for medications known to prolong the QT interval. 12. Uncorrected hypomagnesemia or hypokalemia due to potential effects on the QT interval. 13. Recent (within 14 days before the first dose of SKI-606) or ongoing clinically significant gastrointestinal disorder. 14. Pregnant or breastfeeding women. 15. Evidence of serious active infection, or significant medical or psychiatric illness. 16. Known seropositivity to Human immunodeficiency virus, or current acute or chronic Hepatitis B (HBs antigen positive) or Hepatitis C (HCV antibody positive), cirrhosis, or clinically significant abnormal laboratory finding that would, in the investigator's judgment, make the subject inappropriate for this study.