This is an open-label study of the efficacy of subcutaneous (SC) Abatacept to inhibit progression of structural joint damage in patients with active rheumatoid arthritis (RA) receiving MTX and have inadequate disease control (defined as an ESR based DAS28 ≥ 3.2 AND ≥ 6 swollen and ≥ 6 tender joints). The study consists of a screening period (Days -21 to -7), a baseline visit (Days -20 to -1), and a treatment Period (open label Abatacept 125 mg SC for 24 weeks). All the visits may occur at the indicated week +/- 2 days. The last efficacy assessments are to be conducted at Week 24 and subjects are to be contacted by telephone for a safety follow-up 2 months after the final study agent has been administered.