This study will be conducted in approximately 228 subjects with anemia associated with CKD who are not on dialysis. Two groups of subjects will be enrolled into the study: Group 1: recombinant human erythropoietin (rhEPO) naive subjects; Group 2: rhEPO users, who are currently receiving rhEPO. Subjects who are rhEPO naive will be randomized to receive either GSK1278863 once daily (QD) or rhEPO in a 3:1 fashion; subjects who are receiving an rhEPO before enrolling (rhEPO users) will be randomized in a 1:1 fashion to GSK1278863 QD or to the control arm. For those randomized to the control arm, the decision around whether the subject requires rhEPO, the selection of the type of rhEPO (if needed) and the choice of rhEPO dose to achieve and maintain Hgb concentrations within the target range should be based on Investigator clinical judgment, with the historical rhEPO dose and the current Hgb value being considered. The study consists of a screening phase of at least 4 weeks, a 24-week treatment phase and a follow-up visit that will occur approximately 4 weeks after completing treatment. It is anticipated that the data generated will enable selection of the starting dose(s) and optimize dose adjustment regimen(s) for Phase 3 clinical trials.