The goal of this clinical research study is to see if a new interferon which is given only once a week with ARA-C works as well as standard interferon and low dose ARA-C. The safety of this treatment will also be studied.

If you agree to take part in this study, during treatment, you will have blood tests every 1 to 4 weeks. After 10 years, blood tests are recommended 2 times per year. Bone marrow samples will be taken every 3 months during the first year and then every 3 to 6 months. If you are on this study for 10 years or longer, the bone marrow collections will only be performed if the doctor thinks it is needed. To collect a bone marrow biopsy, an area of the hip is numbed with anesthetic, and a small amount of bone marrow and bone is withdrawn through a large needle.

During treatment, you will receive PEG-Intron once a week. You will also receive Ara-C injections under the skin. You will be taught to inject yourself, or a family member or friend can be taught how to give injections. Treatment will be given to you in the outpatient clinic at MD Anderson or in a clinic close to you.

You will receive treatment as long as it is helping to control the disease. Treatment will go on for about 5 to 20 years.

This is an investigational study. The FDA has approved PEG-Intron only for research studies. About 100 patients will take part in this study. All will be enrolled at MD Anderson.

Inclusion Criteria:

1. Patients age 12 years or older with a diagnosis of Ph-positive or bcr-positive CML in early chronic phase CML (diagnosis < 12 months).
2. Serum bilirubin less than 2mg%, serum creatinine less than 2mg%, and a performance status of 2 or less on Zubrod scale.
3. Patients under age 55 years should have HLA A,B,C, and DR typing performed on themselves and their siblings. Patients under age 20 years and patients with late chronic phase, accelerated phase or blastic phase will be offered allogeneic bone marrow transplantation from a matched sibling as the first priority.

Exclusion Criteria:

1. Severe heart disease (Class III, IV) Psychiatric disability (psychosis) Pregnant or lactating females
2. Women of pregnancy potential must practice birth control methods because of the potential risk of fetal teratogenecity with these agents.
3. Patients must sign an informed consent indicating they are aware of the investigational nature of this study, in keeping with the policies of the hospital.
4. Definition of CML Phases: a. Early chronic phase: time from diagnosis to therapy < 12 months Late chronic phase: time from diagnosis to therapy > 12 months b. Blastic phase: presence of 30% blasts or more in the peripheral blood or bone marrow. c. Accelerated phase CML: presence of any of the following features: - Peripheral or marrow blasts 15% or more - Peripheral or marrow basophils 20% or more - Thrombocytopenia < 100 x 109L unrelated to therapy - Documented extramedullary blastic disease outside liver or spleen
5. Continuation of # 4 d. Clonal evolution defined as the presence of additional clones other than the Ph chromosome is part of accelerated phase CML. Ph chromosome variants or complex Ph chromosome translocations are not considered to indicate disease acceleration. We have recently found clonal evolution to have a variable prognostic impact and may be suppressed with IFN-A therapy (22,23). Hence these patients will be eligible if no other therapy (22,23). Hence these patients will be eligible if no other accelerated phase signs are present.