This study is based on extensive use of BG9588 in non-human primates and pilot evaluation in humans. Up to five patients in each group receiving primary renal allografts will be treated with a 12-month course of BG9588 with or without steroids and mycophenolate to prevent allograft rejection. The recruitment will be performed first in the group with steroids and mycophenolate. Subjects will receive BG9588 at a dose of 70 mg/kg (based on ideal body weight at baseline) via a continuous 60 minute IV infusion within 24 hours pre-operatively followed by a 30 mg/kg dose via a continuous 30 minute IV infusion on the following days: within 24 hours post-transplantation, and on days 3, 10, 18, 28, then monthly through 12 months post-transplantation. The enrollment will be staggered such that early efficacy will be demonstrated in 5 patients prior to completing enrollment. Following 12 months of therapy, patients may be extended to receive additional monthly therapy.