Cancer patients often experience anemia due to the disease itself, chemotherapy, or both. Quality of life is also affected, in part because of the fatigue associated with anemia. Previous studies with epoetin alfa have suggested that achieving a higher hemoglobin level may improve the quality of life and help patients live longer. This is a 12-week, double-blind, placebo-controlled, multicenter study to determine the effect of treatment with epoetin alfa on the percentage of red blood cells in anemic patients with chronic white blood cell leukemia. At the start of the study, patients were either receiving no chemotherapy, single-agent chemotherapy, and/or were on prednisone (steroid) treatment. Patients will be randomly assigned 2:1 to receive either epoetin alfa or placebo. Patients receiving epoetin alfa will receive subcutaneous (under the skin) epoetin alfa injections 3 times per week and patients on placebo will receive an equal volume of matching placebo, injected subcutaneously 3 times per week. Based on patients' rate of increase in red blood cell percentage, the original dose of 150 units per kilogram 3 times per week may be raised gradually to 300 units per kilogram 3 times per week, to reach a target red blood cell percentage of 38% to 40%. Patients achieving the target red blood cell percentage will be eligible for a 12-week open-label extension of the study, which will focus on safety findings. Effectiveness will be determined by the proportion of patients who reach the target red blood cell percentage of 38% to 40% by the end of the study, the number of transfusions required, the proportion of patients achieving a red blood cell percentage of 38% to 40% at any time during the study, and changes in quality of life parameters. Safety evaluations, including the incidence of adverse events, laboratory tests, and vital signs, will be performed throughout the study. The hypothesis of the study is that epoetin alfa will be superior to placebo in increasing the percentage of red blood cells to the target level, reducing the number of transfusions required, and improving the quality of life. Epoetin alfa 150 units per kilogram 3 times weekly subcutaneously for 12 weeks. Individualized dose increases of 50 mg/week depend on red blood cell response, up to a maximum 300 units per kilogram 3 times per week to obtain the target level of 38% to 40% red blood cells.