Renal Allograft Tolerance Through Mixed Chimerism (Belatacept)

Inclusion Criteria: * Male or female 18-60 years of age * Candidate for a living-donor renal allograft from an HLA mismatched donor * First or second transplant with either a living donor or cadaveric transplant as the first transplant. * Use of FDA-approved methods of contraception by all recipients from the time that study treatment begins until 104 weeks (24 months) after renal transplantation. * Ability to understand and provide informed consent. * Serologic evidence of prior exposure to EBV. Exclusion Criteria: * ABO blood group-incompatible renal allograft. * Evidence of anti-HLA antibody within 60 days prior to transplant as assessed by routine methodology (AHG and/or ELISA) * Leukopenia or thrombocytopenia. * Positive for HIV-1, hepatitis B core antigen, or hepatitis C virus; or positivity for hepatitis B surface antigen. * Cardiac ejection fraction \< 40% or clinical evidence of insufficiency. * Forced expiratory volume FEV1 \< 50% of predicted. * Lactation or pregnancy. * History of cancer other than basal cell carcinoma of the skin or carcinoma in situ of the cervix. * Underlying renal disease etiology with a high risk of disease recurrence in the transplanted kidney (such as focal segmental glomerulosclerosis, type I or II membranoprolifertive glomerulonephritis). * Prior dose-limiting radiation therapy. * Known genetic disease or family history that may result in greater sensitivity to the effects of irradiation, or a physical deformity that would preclude adequate shielding or appropriate dosing during the irradiation component of the conditioning regimen. * Enrollment in other investigational drug studies within 30 days prior to enrollment. * Abnormal (\>2 times lab normal) values for (a) liver function chemistries (ALT, AST, AP), (b) bilirubin, (c) coagulation studies (PT, PTT). * Allergy or sensitivity to any component of belatacept, ATG, tacrolimus, or rituximab. * Maintenance immunosuppression within 3 months prior to conditioning other than physiological doses of steroids, defined as ≤ 50 mg of hydrocortisone or dose equivalent. * The presence of any medical condition that the investigator deems incompatible with participation in the trial.