Kidney transplantation is a good treatment option for people with kidney disease. However, there is still much to learn about how to best care for the transplanted kidney and keep it functioning for a long time. Transplant recipients take immunosuppression (anti-rejection) drugs to prevent their body from rejecting the new kidney. These drugs are used to prevent the immune system from attacking the transplanted kidney. All anti-rejection medications have unwanted side effects. The purpose of this study is to evaluate the safety of slowly removing tacrolimus therapy after treatment with ATG. The study will compare how well transplanted kidneys work and the response of people's immune systems as tacrolimus is stopped. In addition, this research study will evaluate whether reducing immunosuppression can decrease some of these side effects while still preventing rejection of the kidney.