Patients in cohort 2 receive an escalated dose of oblimersen; if well tolerated, subsequent cohorts receive oblimersen at the higher dose with the original dose of imatinib mesylate. If oblimersen is not well tolerated in cohort 2, subsequent cohorts receive the original dose of oblimersen with an escalated dose of imatinib mesylate. The first 6 patients accrued continue to receive the original dose (dose taken prior to study) of imatinib mesylate throughout the study.