The Stanford Medical Center Program in Multi-Organ Transplantation and the Division of Bone marrow Transplantation are enrolling patients into a research study to determine if donor stem cells given after a living related one Haplotype match kidney transplantation will change the immune system such that immunosuppressive drugs can be completely withdrawn.

The goal of this study is for the recipients of a living related kidney transplant of one HLA haplotype to be withdrawn of immunosuppressive medication and become "tolerant "to their kidney graft. The recipient will receive a conditioning regimen composed of low dose radiation to the lymphoid tissue (total lymphoid irradiation, TLI) and anti-thymocyte globulin (ATG) at the time of transplant. They will then be infused with purified "stem cell" and T-cell from their kidney donors 2 weeks after the transplant to try to achieve mixed chimerism of their white blood cells with the donor (the recipient would have a mixture some of the with blood cells of the donor and theirs in their blood). The kidney donor has to provide peripheral stem cell 6-8 weeks before kidney donation. It is an outpatient procedure done using peripheral veins after treatment with G-CSF (filgrastim).Immunosuppressive medication will be decreased gradually and possibly stopped by 1 1/2 year after the transplantation if the recipient meets withdrawing criteria (persistence of mixed chimerism more than 18 months, no episode of rejection and no rejection on surveillance kidney biopsy). Potential candidates need to be approved for kidney transplant and available for close follow-up at Stanford University Medical Center.

Inclusion Criteria:

1. All consenting adults who are 18 to 60 years, living donor transplant candidates and have a haplotype related living donor or > 2 HLA antigen matched, unrelated, living donor (including at least one HLA-DR antigen match plus at least one antigen match of either HLA-A or HLA-B).
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 post-transplant.
5. ABO compatible.

Exclusion Criteria:

1. Previous treatment with rabbit ATG or a 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 than 80% or demonstration of donor specific antibody (DSA).
8. Prior organ transplantation.
9. High risk of primary kidney disease recurrence (e.g atypical HUS). However, patients with primary FSGS will not be excluded.