This study is a Phase 3 single center, uncontrolled trial in which 1-3 allogeneic pancreatic islet transplants are performed for each study subject. Follow-up evaluations after transplant continue for 52 weeks after the final islet transplantation. Thereafter, subjects may enroll for a 5-year follow-up study and an additional 5 year to 10 year follow-up study to evaluate the function of the islets and to measure and regulate immunosuppressive drug levels and side effects.