Under current standard of care procedure, islets are transplanted into patient's liver. The investigators have learned that some of these cells do not survive the current procedure and are lost around the time of transplant. Therefore in this study, the investigators are studying a new transplant procedure that may help prevent this islet cell loss. The new procedure involves transplanting the islets into an omental pouch instead of into the liver. The omentum is a large apron-like fold of membrane inside the abdomen that drapes over the intestines. This study will test to see if omental islet transplantation is safe and effective. Standard immunosuppressive medicines (anti-thymocyte globulin, tacrolimus, mycophenolic acid, sirolimus, etanercept) will be used in this study to prevent rejection of the islets.