Existing pre-clinical and clinical data suggest that SCH66336, a farnesyl transferase inhibitor,exhibits significant activity against CML cells, and in fact may have synergistic activity in combination with imatinib mesylate. Thus, the objectives to the study are (1) to determine the maximum tolerated dose (MTD) and dose limiting toxicities (DLT) of lonafarnib (SCH66336), a farnesyl transferase inhibitor, in combination with imatinib mesylate (Gleevec) in patients with chronic phase, accelerated phase, and blast crisis CML; (2) to assess the pharmacokinetics of the combination of lonafarnib and Gleevec in these patients; and (3) to assess in a preliminary way the biologic activity of the combination of lonafarnib and Gleevec in these patients.