This clinical study is investigating AMG 719, an investigational drug, for the treatment of patients who have Rheumatoid Arthritis and who are taking Methotrexate. AMG 719 is a drug which is self-injected beneath the skin (similarly to the way insulin is self-injected by diabetics). Patients on this study are on study for 28-weeks. They visit the study facility at least 11 times while participating in the study.