The goal of this clinical research study is to find the highest safe dose of the drugs ZarnestraTM (R115777) and Gleevec (imatinib mesylate) that can be given in combination for the treatment of chronic myelogenous leukemia (CML) in chronic phase. The effect of this combination on the leukemia will also be studied.

R115777 is a new drug that blocks the function of an enzyme that is important in making some proteins work. One of the most important targets for this enzyme is a protein that can make cells become cancer. Imatinib mesylate is a drug that blocks the function of the protein that comes from the Philadelphia chromosome. The Philadelphia chromosome is an abnormality in chromosomes 9 and 22 that changes blood cells into leukemia cells.

Before treatment starts, participants will have a physical exam, blood tests (About 3 tubes, 2 teaspoons each), and a bone marrow biopsy. The bone marrow will be removed with a large needle.

Participants in this study will take imatinib mesylate by mouth every day for as long as they stay on study, which means as long as it works. Participants will also take R115777 twice a day for 2 weeks. This will be repeated every 3 weeks. The amount of each of these medications that participants take will depend on when they enter the study. The doses will be slowly increased from participant to participant until the highest dose that does not cause serious side effects is found.

Participants will be asked to visit their doctor for a physical exam and measurement of vital signs. The frequency of doctor visits will vary depending on physical condition. Blood tests (about 2 teaspoons each) will be done every week during the first 3 weeks of treatment. Blood tests will then be done every 8-12 weeks for the length of the study, as needed. The blood samples will be used for routine lab tests. A bone marrow sample will also be taken to check and measure cells related to the disease every 3 months in the first year and then every 6-12 months. Participants can stay on study for as long as the treatment is considered to be beneficial. Participants will be taken off study if their disease gets worse or intolerable side effects occur.

This is an investigational study. The FDA has authorized the use of imatinib mesylate for patients with CML. It is the combination of imatinib mesylate and R115777 that is experimental. R115777 has been authorized for investigational use only. A maximum of 30 patients will take part in this study. All will be enrolled at M. D. Anderson.

Inclusion Criteria:

• Patients 16 years or older with Philadelphia chromosome (Ph)- or BCR/ABL-positive CML (as determined by cytogenetics, FISH, or PCR) are eligible if they are not candidates for known regimens or protocol treatments of higher efficacy or priority. Patients must be in the chronic phase of CML.
• Patients must have failed therapy with imatinib mesylate. Failure will be defined as: 1) patients who have failed to achieve or have lost a complete hematologic remission at 3 months from the start of therapy with imatinib mesylate, or 2) patients who have failed to achieve or have lost at least a minimal cytogenetic response after 6 months of therapy with imatinib mesylate, or 3) patients who have failed to achieve or have lost a major cytogenetic response after 12 months of therapy with imatinib mesylate
• Chronic phase will be defined by the following features: 1) blasts in peripheral blood or bone marrow <10%, 2) basophils in PB or BM <20%, 3) platelets >100 x 10(9)/L, 4) absence of clonal evolution
• Patients must sign an informed consent
• Performance status \