In this study, LY2127399 will be tested as a potential treatment to reduce the blood proteins in some patients with End-Stage Renal Disease (ESRD). These proteins are called alloantibodies and are made by the body to react with other proteins called HLA proteins. When a person has these antibodies, they are referred to as HLA-presensitized. Often the presence of these antibodies, measured by a test called the PRA (panel reactive antibody), can make a person ineligible to receive a transplant - or experience very long wait times on the kidney transplant waiting list. Therefore the need to reduce the antibodies is significant for the successful treatment of ESRD. This study will treat ESRD patients for 6 months with LY2127399 and measure PRA levels for a total of 18 months.