A new immunosuppressive drug, based on the inhibition of an important enzyme in the immune system called JAK3, is being developed by Pfizer to prevent transplant rejection. In this research study, a JAK3 inhibitor or tacrolimus will be given to new kidney transplant patients for 6 months. Patients who respond well will be offered the opportunity to participate in an additional study to receive the JAK3 inhibitor or tacrolimus long-term. There will be 2 stages of enrollment in this study. In both stages of this research study, patients will be assigned to one of three treatment groups from the day after receiving a kidney transplant. Two of the treatment groups will be 2 different dose levels of the JAK3 inhibitor that will be taken by mouth. The third treatment group will be twice daily tacrolimus (Prograf). Patients will continue to take the assigned study medication (JAK3 inhibitor or tacrolimus) for 6 months as well as other standard transplant medications such as Cellcept and prednisone.