This research study is to determine if donor blood stem cells given after living, related, HLA antigen (Ag) haplotype match or living, unrelated donor kidney transplantation. Minimal HLA antigen matching will include matching of 2 HLA antigens that can be either HLA A, B, and /or DR. This research will change the immune system such that immunosuppressive drugs can be completely withdrawn or reduced to minimal dose without kidney rejection.

The objectives of this study are to determine whether patients undergoing kidney transplants for end stage renal disease (ESRD) can be taken off immune suppression drugs given to prevent kidney rejection or can be maintained on low dose immune suppression while maintaining normal kidney function. Patients will receive blood stem cell transfusions from their donors 11 days after transplant to reduce the risk of graft rejection while tapering the post-transplant immune suppression drug regimen. Patients will be treated with total lymphoid irradiation (TLI) and rabbit anti-thymocyte globulin (rATG) followed by transfusion of enriched CD34+ hematopoietic cells containing blood stem cells and CD3+ T cells from their donors in order to induce blood cell mixed chimerism. These chimeric patients produce blood cells from both their own and their donors' blood stem cells. Donors will have blood collected by apheresis after treatment with drugs to "mobilize" blood stem cells from their bone marrow. Collection of the donor's cells will occur 6-8 weeks before kidney donation surgery. After transplant, patients will receive a 14 week course of corticosteroid therapy (e.g., Prednisolone) with gradual dose reduction. They will also receive a 12 month course of mycophenolate mofetil (MMF) with dose tapering beginning 9 months post-transplant and an 18 month course of Tacrolimus with tapering also beginning at 9 months post-transplant. Patients will be monitored for renal function, mixed blood cell chimerism, the appearance of donor specific antibodies (DSA) from their own immune cells reacting to the transplanted kidney, and evidence of rejection in any biopsies of the donor kidney after transplant. Immune suppression drug withdrawal will begin and continue as long as mixed chimerism is maintained, the patient shows no evidence of graft versus host disease (GVHD), the transplanted kidney functions well, and there is no indication of kidney rejection in biopsies. Patients not meeting these criteria will be maintained on low dose immunosuppressive drug therapy unless more extensive treatments are needed to prevent rejection. Potential candidates need to be approved for kidney transplant under this protocol and available for close follow-up post-transplant. This study, sponsored by the California Institute for Regenerative Medicine (CIRM), is being conducted in parallel with NCT01165762 sponsored by the National Institutes of Health with distinct reporting and separation of funding support for the patients enrolled under each sponsor.

Inclusion Criteria:

1. All consenting adults (18 years of age) living donor renal transplant recipients at Stanford University Medical Center who have a one haplotype match donor.
2. Patients who agree to participate in the study and sign an Informed Consent.
3. Patients who have no known contraindication to administration of rabbit ATG or radiation.
4. Males and females of reproductive potential who agree to practice a reliable form of contraception for at least 24 months posttranplant.

Exclusion Criteria:

1. Previous treatment with rabbit ATG or known allergy to rabbit proteins.
2. History of malignancy with the exception of non-melanoma skin malignancies.
3. Pregnant women or nursing mothers.
4. Serological evidence of HIV, Hepatitis B or Hepatitis C infection.
5. Seronegative for Epstein-Barr virus , if donor is seropositive.
6. Leukopenia (with a white blood cell count < 3000/mm3) or thrombocytopenia (with a platelet count < 100,000/mm3)
7. Panel Reactive antibody greater then 20% or demonstration of donor specific antibody (DSA).
8. Prior organ transplantation.
9. High risk of primary kidney disease recurrence (i.e. primary FSGS).