 Every 4 weeks, the study medicine Homoharringtonine will be given by vein daily for 5 days along with continuing daily doses of the approved medicine Gleevec taken by mouth. The safety and effectiveness of this combined treatment in CML patients will be studied. Patients who do not achieve a meaningful hematologic or cytogenetic response after 4 cycles or less will be discontinued. Otherwise, patients may continue additional cycles of this combined treatment for a maximum of 12 cycles. 