There will be a maximum of 2 screening visits before study treatment, a baseline visit (Day 0), and 11 study visits. A physical exam, assessment for adverse events, and blood collection will occur at all study visits. Kidney and liver function tests and rheumatologic evaluations will occur at most study visits; participants will also be asked to complete a questionnaire on their health at most study visits. Arthroscopy (knee biopsy) on the more inflamed knee will occur at baseline and Month 3. Participants will be contacted by telephone the day after each arthroscopy and rituximab infusion.