This phase II trial studies how well giving imatinib mesylate together with chemotherapy and peripheral stem cell transplantation works in treating patients with newly diagnosed acute lymphoblastic leukemia. Drugs used in chemotherapy use different ways to stop cancer cells from dividing so they stop growing or die. Imatinib mesylate may stop the growth of cancer cells by blocking the enzymes necessary for cancer cell growth. Giving imatinib mesylate together with chemotherapy and peripheral stem cell transplantation may be an effective treatment for acute lymphoblastic leukemia.