This is a phase I study to assess the safety and tolerability of infusing expanded stem cells into the pancreas of patients with type I diabetes and a successful renal transplant. The stem cells used in this study occur naturally in the body and are collected from each recipient by a procedure called leukapheresis. The cells are then expanded and differentiated into insulin-like cells in a sterile suite before being injected into the body or tail of the pancreas of the recipient.