During the first part of this study, patients will receive different amounts of DCC-2036 to determine the highest safe dose. Multiple dose levels of DCC-2036 will be tested and as long as no medically unacceptable side effects are noted, the dose will be increased for the next group of study patients. When the highest dose is reached, a larger number of patients will be enrolled to receive DCC-2036 at the highest (safe) dose level. Additional study patients will be enrolled in a group called an "Expansion Group" and receive the study drug at the highest well tolerated dose. Evaluation of the safety and efficacy (how well the study medication treats leukemia) will be studied in this trial. Disease assessment will be monitored as follows: (1) Blood samples will be collected for disease response and for mutational analysis if disease has gotten worse (progressed); (2) Bone marrow samples may be collected by having an area of the hip or chest bone numbed with an anesthetic and a small amount of bone marrow drawn through a needle; (3) For CML patients only, blood samples will be collected for BCR-ABL transcript levels. Patient safety is of primary importance in this Phase 1 study. Safety assessment will be monitored as follows: (1) Physical examinations will be performed regularly during your doctor's visits; (2) Routine blood tests will be performed on a regular basis to assess potential side effects that may be caused by study medication on different organs like (and not limited to) liver, kidney and bone marrow; (3) Based on reports of potential side effects to the heart that may be caused by study medication, patients will be required to have echocardiograms and blood draws to measure the level of serum N-terminal fragment pro B-type natriuretic peptide (NT-proBNP). An echocardiogram is a noninvasive test that uses sound waves to produce images of your heart. These images will tell the doctor how a patient's heart is beating and pumping. The NT-proBNP is a blood test that will help the patient's doctor evaluate how well the heart works. After initial testing is completed, patients will then be required to have these safety evaluations performed at intervals of 3-cycles (approximately every 3 months) for as long as they are taking the study medication. Patients who experience muscle weakness or peripheral neuropathy will be assessed by blood draws to measure creatine phosphokinase (CPK) levels. Measuring CPK levels may help the patient's doctor determine whether or not the symptoms they are experiencing are the result of muscle damage or due to other causes. The most common eye disorders include blurred vision, dry eyes, and visual impairment. Patients will be required to have complete eye (ophthalmologic) evaluations. After initial ophthalmologic exams, patients will be required to have an exam after the completion of every 3 cycles of study medication (approximately every 3 months) and at the time they stop taking study medication. Blood samples will be collected for pharmacokinetic analysis. Pharmacokinetics is the study of the bodily absorption, distribution, metabolism, and excretion of drugs. Blood samples will also be collected for pharmacodynamic analysis. Pharmacodynamic analysis measures biomarkers that are either proteins or genes (also called DNA) that are associated with a disease that may also be related to how you respond to a treatment or what type of side effects may happen. The investigational drug DCC-2036 has not been approved by the United States Food and Drug Administration (FDA). The FDA allows DCC-2036 to be used in research studies only. DCC-2036 will be given to patients only during this study and not after the study is over.