Subjects for the study will be made up of non-human primates (monkeys) and humans. Up to 5 subjects in each of the groups receiving kidney transplants will be placed on a 12 month course of BG9588 with or without additional anti-rejection drugs. BG9588 will be given intravenously (injected through a vein) prior to the transplant and then in a decreased dose with a decreased frequency over the year. Following the 12 months of therapy subjects may be eligible for additional monthly therapy.