A Study to Assess the Safety, Tolerability and Pharmacokinetics of Multiple Subcutaneous Injections of ABBV-257 in Subjects With Rheumatoid Arthritis

* Diagnosis of Rheumatoid Arthritis based on the 2010 American College of Rheumatology (ACR)/European League against Rheumatism (EULAR) criteria, or ACR 1987 for patients with diagnosis prior 2011 ≥ 3 months. * Except for methotrexate (MTX), the subject must have discontinued all disease modifying anti-rheumatic drugs (DMARD) for at least 5 half-lives before the first dose of study drug, and undergone cholestyramine washout if received Leflunomide within the past 3 months. * Subject must have been on MTX therapy \> 3 months and on a stable dose (7.5 - 25 mg/week), for at least 4 weeks prior to the first dose of study drug. Subject must be able to continue on stable dose of MTX for the duration of study participation. * Body Mass Index (BMI) is 19 to 35, inclusive. (BMI is calculated as weight \[kg\] divided by height \[m2\].) * Judged to be in good general health as determined by the Investigator based upon the results of medical history, laboratory profile, physical examination and 12-lead electrocardiogram (ECG) performed at screening

* Evidence of anti-ABBV-257 antibody results in a pre-study serum sample. * History of significant allergic reaction or significant sensitivity to any constituents of the study drug; or history of anaphylactic reaction to any agent (e.g., food products and bee sting); or history of a major reaction to any Immunoglobulin G (IgG) containing product. * History of persistent chronic or active infection(s) requiring hospitalization or treatment with intravenous or oral antimicrobials/antibiotics within 30 days prior to initial study drug administration. * History or evidence of active tuberculosis (TB) or the subject has evidence of risk factor for latent TB. * Clinically significant abnormal screening laboratory results as evaluated by the Investigator, including serum values of Aspartate aminotransferase (AST) or Alanine aminotransferase (ALT) greater than 2.25 × the upper limit of normal, or creatinine greater than 1.5 × the upper limit of normal, or absolute neutrophil count \< 1500 μ/L. * Subject has any medical condition or illness other than RA that is not well controlled with treatment that would, in the opinion of the investigator, preclude study participation or interfere with other symptoms of Rheumatoid Arthritis (RA).