This protocol is an open label, non-randomized study designed to test whether treatment with BG9588, a humanized monoclonal antibody specific for CD154, can induce a state of allograft tolerance following renal allotransplantation in humans. This study is designed to primarily assess the safety and efficacy of BG9588 when given alone or in combination with steroids and mycophenolate to prevent renal allograft rejection without the use of calcineurin inhibitors or other chronic anti-rejection therapies. Efficacy parameters will include the incidence of acute and chronic rejection episodes, and immunological graft loss. Additional evaluation will be performed to specifically assess the development of donor-specific immune hyporesponsiveness resulting from the use of BG9588.