This study will compare the efficacy and safety of subcutaneous Mircera and subcutaneous darbepoetin in the treatment of renal anemia in participants with chronic kidney disease who are not on dialysis and not receiving erythropoiesis-stimulating agents (ESA). Participants will be randomized to receive either Mircera once every 4 weeks, at a starting dose of 1.2 micrograms/kilogram (mcg/kg), or darbepoetin alfa once weekly, at a starting dose of 0.45 mcg/kg (or once every two weeks, 0.75 mcg/kg). The anticipated time on study treatment is 3-12 months.