Participants will undergo a kidney transplant. Before the surgery, a central line (intravenous catheter), through which blood and medicine can be given, is placed in the neck or chest. Patients may also undergo leukapheresis, a procedure for collecting white blood cells. The cells can be stored for transfusion later if white cell counts drop following Thymoglobulin treatment. For this procedure, blood is drawn from a needle placed in the arm and flows into a machine that separates the blood components by spinning. The white cells are collected in a bag and the red cells and plasma are returned through a second needle in the other arm.