Chemotherapy and Peripheral Stem Cell Transplantation Followed by Immunotherapy in Treating Patients With Chronic Myelogenous Leukemia

RATIONALE: Drugs used in chemotherapy use different ways to stop cancer cells from dividing so they stop growing or die. Combining chemotherapy with a peripheral stem cell transplant and immunotherapy may allow the doctor to give higher doses of chemotherapy drugs and kill more cancer cells. Biological therapies use different ways to stimulate the immune system and stop cancer cells from growing. PURPOSE: This phase II trial is studying giving chemotherapy together with a peripheral stem cell transplant followed by immunotherapy to see how well it works in treating patients with chronic phase chronic myelogenous leukemia.