This Phase II trial will evaluate at least 100 patients for the rate of complete or major cytogenetic response of STI571 as demonstrated by a decrease in the percentage of Ph chromosome positive cells in the bone marrow in patients with CML who are refractory to or intolerant of interferon-alpha. Statistical considerations are based on the refractory patient population only. Intolerant patients are included as long as recruitment of the refractory patients is ongoing, up to a maximum of 100 intolerant patients, whichever comes first.