RecruitingBiological interventionStudy of Combined Kidney and Blood Stem Cell Transplant From a Brother or Sister DonorThe purpose of this study is to find out if an investigational treatment will allow kidney transplant recipients to better accept their new kidney and stop immunosuppressive medicines. This study is for kidney transplant recipients who receive a kidney from a sibling donor. The investigational treatment is started after kidney transplant. It begins with a regimen of a drug called rabbit anti-thymocyte globulin (rATG) combined with radiation therapy (known as total lymphoid irradiation, or TLI) to the lymph nodes and spleen. This is followed by an infusion of blood stem cells, which will be donated by the same sibling who donated their kidney. Researchers think that this treatment allows immune cells from the donor and recipient to live side by side, a condition referred to as "mixed chimerism." Mixed chimerism may help create a state of "tolerance" in kidney transplant recipients in which all immunosuppressive medications can be stopped without rejection of the transplanted kidney. This study will test whether (1) the investigational treatment will allow patients to stop immunosuppressive medications after their kidney transplant and (2) if the treatment impacts the rate of kidney rejection and the side effects of immunosuppressive medications.