This phase II trial studies how well dasatinib, nilotinib, and imatinib mesylate works in treating patients with newly diagnosed, previously untreated chronic myeloid leukemia in which fewer than 10% of the cells in the blood and bone marrow are blast cells (immature blood cells) (chronic phase). Dasatinib, nilotinib, and imatinib mesylate may stop the growth of cancer cells by blocking some of the enzymes needed for cell growth.