This study will test the safety and effectiveness of two drugs, Sirolimus and Thymoglobulin, for preventing rejection of transplanted kidneys. Standard anti-rejection therapy uses a combination of drugs, such as cyclosporine, tacrolimus, azathioprine, steroids, and others, that are taken daily for life. However, even with this daily therapy, more than half of kidney recipients slowly reject their transplant within 10 years. Both Thymoglobulin, an antibody, and Sirolimus, an anti-rejection drug, prevent rejection by lowering the response of the immune system to the transplanted organ. Thymoglobulin is given in the pre- and postoperative period, and Sirolimus is taken long term.