LEA29Y (Belatacept) Emory Edmonton Protocol

Inclusion Criteria: * Mentally stable and able to comply with study procedures * Clinical history compatible with type 1 diabetes with onset of disease at less than 40 years of age, insulin dependence for at least 5 years at study entry, and a sum of age and insulin dependent diabetes duration of at least 28 * Absent stimulated C-peptide (less than 0.3 ng/mL) 60 and 90 minutes post-mixed-meal tolerance test * Involvement of intensive diabetes management, defined as: 1. Self-monitoring of glucose no less than a mean of three times each day averaged over each week 2. Three or more insulin injections each day or insulin pump therapy 3. Under the care of an endocrinologist, diabetologist, or diabetes specialist with at least three clinical evaluations during the past 12 months prior to study enrollment * At least one episode of severe hypoglycemia, defined as an event with one of the following symptoms: memory loss; confusion; uncontrollable behavior; irrational behavior; unusual difficulty in awakening; suspected seizure; seizure; loss of consciousness; or visual symptoms, in which the participant was unable to treat him/herself and which was associated with either a blood glucose level less than 54 mg/dL or prompt recovery after oral carbohydrate, intravenous glucose, or glucagons in the 12 months prior to study enrollment * Reduced awareness of hypoglycemia. More information about this criterion is in the protocol. Exclusion Criteria: * Body mass index (BMI) greater than 30 kg/m\^2 or weight less than or equal to 50 kg (110 lbs) * Insulin requirement of more than 1.0 IU/kg/day or less than 15 U/day * HbA1c greater than 10% * Untreated proliferative diabetic retinopathy * Systolic blood pressure higher than 160 mmHg or diastolic blood pressure higher than 100 mmHg * Measured glomerular filtration rate using iohexol of less than 80 mL/min/1.73m\^2. * Presence or history of macroalbuminuria (greater than 300 mg/g creatinine) * Presence or history of panel-reactive anti-Histocompatibility Antigen (HLA) antibody levels greater than background by flow cytometry. More information about this criterion is in the protocol. * Pregnant, breastfeeding, or unwilling to use effective contraception throughout the study and 4 months after study completion * All women more than 35 years and women of any age who have first degree relatives with a history of breast carcinoma or who have other risk factors of breast carcinoma. More information about this criterion is in the study protocol. * Active infection, including hepatitis B, hepatitis C, human immunodeficiency virus (HIV). Presence or history of tuberculosis. More information about these criteria is in the protocol. * Negative for Epstein-Barr virus (EBV) by anti-viral capsid antigen (VCA) IgG (EBV VCA-IgG) determination * Invasive aspergillus, histoplasmosis, or coccidioidomycosis infection in the past year * History of malignancy except for completely resected squamous or basal cell carcinoma of the skin * Known active alcohol or substance abuse * Baseline Hgb below the lower limits of normal, lymphopenia, neutropenia, or thrombocytopenia * History of Factor V deficiency * Any coagulopathy or medical condition requiring long-term anticoagulant therapy after transplantation or individuals with an international normalized ratio (INR) greater than 1.5. * Severe coexisting cardiac disease, defined as: 1. Heart attack within the last 6 months 2. Evidence of ischemia on functional heart exam within the year prior to study entry 3. Left ventricular ejection fraction less than 30% * Persistent elevation of liver function tests at study entry * Symptomatic cholecystolithiasis * Acute or chronic pancreatitis * Symptomatic peptic ulcer disease * Severe unremitting diarrhea, vomiting, or other gastrointestinal disorders that could interfere with the ability to absorb oral medications * Hyperlipidemia despite medical therapy, defined as fasting LDL cholesterol greater than 130 mg/dL and/or fasting triglycerides greater than 200 mg/dL * Currently receiving treatment for a medical condition that requires chronic use of systemic steroids except for the use of 5 mg or less of prednisone daily, or an equivalent dose of hydrocortisone, for physiological replacement only * Treatment with any antidiabetic medication other than insulin within the past 4 weeks * Previous receipt of belatacept * Use of any investigational agents within the past 4 weeks * Received a live attenuated vaccine(s) within the past 2 months * Any medical condition that, in the opinion of the investigator, might interfere with safe participation in the trial * Treatment with any immunosuppressive regimen at the time of enrollment. * A previous islet transplant. * A previous pancreas transplant, unless the graft failed within the first week due to thrombosis, followed by pancreatectomy and the transplant occurred more than 6 months prior to enrollment. * Known hypersensitivity to mycophenolate mofetil or any of its components * Imprisonment or involuntary incarceration for treatment of either a psychiatric or physical illness * Rare hereditary deficiency of hypoxanthine-guanine phosphoribosyltransferase (HGPRT) such as Lesch-Nyhan and Kelly-Seegmiller syndrome * Dietary restriction of phenylalanine