Zarnestra and Gleevec in Chronic Phase Chronic Myelogenous Leukemia

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 \</= 2 by Zubrod scale
* Patients must have adequate hepatic functions (bilirubin \</= 2.0 mg/dl) and renal functions (creatinine \</=2 mg/dl)
* WBC \</= 30 x 10(9)/L. Patients may receive Hydroxyurea (or other similar agent) to bring the WBC below this level. Hydroxyurea (or its equivalent) must be discontinued 24 hours before the start of therapy.
* Patients of childbearing potential should practice effective methods of contraception.

Exclusion Criteria:

* Patients under 16 years of age.
* Pregnant and nursing females will be excluded.