The purpose of this study is to explore whether LY2127399 is effective in relieving signs and symptoms of rheumatoid arthritis (RA) in patients with a history of inadequate response or intolerance to at least 1 Tumor Necrosis Factor-Alpha (TNFα) inhibitor therapy. Examples of these TNFα inhibitor therapies that are currently on the market include Enbrel® (etanercept), Remicade® (infliximab), and Humira® (adalimumab).