The purpose of this study is to compare the outcomes of patients with CKD randomly assigned to 2 treatment groups, which differ only in their targeted hemoglobin levels. This study will test the primary hypothesis that the level of anemia correction with once weekly dosing of PROCRIT® (Epoetin alfa) in patients with chronic kidney disease will decrease mortality and cardiovascular morbidity. Patients will receive a starting dose of PROCRIT® 10,000 Units (U) subcutaneously (SC) 1x / week. After 3 weekly doses, subsequent doses and dosing intervals of PROCRIT®, up to a maximum dose of 20,000 U for 36 months, will be adjusted based on an assessment of the two most recent hemoglobin values.