Patients receive oblimersen IV continuously on days 1-10 and oral imatinib mesylate once or twice daily. Treatment repeats every 21 days for up to 4 courses in the absence of disease progression or unacceptable toxicity. Patients without a hematologic response after 2 courses go off study. Patients with complete or partial response after 4 courses may continue to receive oral imatinib mesylate daily.