Rheumatoid arthritis (RA) is a chronic inflammatory disease characterized by joint swelling, pain, stiffness, damage, and ultimately loss of joint function. Scientists estimate that about 1.3 million people (0.6 percent) of the U.S. adult population have RA. Current therapies target the immune system early in the disease process before joint damage occurs, and include drugs such as methotrexate (MTX) and tumor necrosis factor (TNF)-blocking agents. Rituximab is a disease-modifying antirheumatic drug (DMARD) recently approved by the FDA for use in combination with MTX for treatment of moderately to severely active RA in patients who have had an inadequate response to TNF-blocking agents, in an effort to try to slow the course of the disease. This study will examine the effects of rituximab on the immune response and disease activity in participants with early RA who have not been treated with any disease-modifying agent. In addition, the safety and tolerability of rituximab in this population will be examined.