This is a phase II multicenter, open-label study designed to investigate the feasibility (tolerance, compliance and safety) of a combination of the tyrosine kinase inhibitor STI 571 (GLIVEC, Novartis Pharma) with a pegylated *-Interferon 2b (PEG INTRON). The rationale for testing this combination is that 1) aIFN is curently the first line agent for the treatment of CML, 2) the pegylated formulation of aIFN is more convenient and is better tolerated than the conventional formulation, 3) STI571 is currently the most promising investigational agent for the treatment of CML because it is targeted to the molecular bases of the disease, is effective also in the advanced phases of the disease, and is effective also in the cases who are resistant to aIFN, 4) the mechanisms of action of the two agents are different. Therefore the combination of STI571 and PEGINTRON is likely to provide the best treatment of CML and to be tested very soon in randomized phase III studies of efficacy. So far STI571 and PEGINTRON have been investigated separately. The present study is an exploratory study that has been planned with the aim of evaluating the adverse events and the safety of the combination, so as to identify a safe and tolerable regime that can be tested prospectively for efficacy in a subsequent, randomized phase III study. Based on available knowledge and data, STI571 is more specific and can be more effective than PEGINTRON. Therefore in this exploratory study STI571 is given a priority over PEGINTRON as to dose and dose adaptation. Sixty subjects with chronic phase CML, previously untreated with any one of study drugs, will be enrolled over a 3 months period and will be treated and studied for 12 months. The patients can be pretreated with hydroxyurea , whenever required, hence are treated with STI 571 at a fixed dose (400mg) and with PEG-Intron at doses ranging from 50 to 150 *g weekly (the first cohort of 20 patients at 50 *g/w, the second cohort of 20 patients at 100 *g/w and the third cohort of 20 patients at 150 *g/w). The response (hematologic, cytogenetic and molecular) to the combination treatment will be evaluated every 3 months, and the pharmacokinetics of study drugs will be studied in a sample of study patients. The duration of the study is 12 months, for a total trial time of 15 months.