OUTLINE: Patients receive oral imatinib mesylate (STI-571) once daily for 9 months. At 9 months, patients with more than 35% Philadelphia chromosome-positive (Ph+) cells in bone marrow receive oral STI-571 twice daily for 3 more months. At 12 months, patients with more than 35% Ph+ cells in bone marrow receive oral STI-571 once daily and interferon alfa subcutaneously once daily. Treatment continues for at least 1 year in the absence of disease progression or unacceptable toxicity. Patients with an appropriate HLA-matched donor may choose to have a bone marrow transplantation at any time during the study.