A Study of Baricitinib (LY3009104) in Participants With Rheumatoid Arthritis (RA)

Inclusion Criteria: * Have a diagnosis of adult-onset RA as defined by the ACR/European League Against Rheumatism (EULAR) 2010 Criteria for the Classification of RA. * Have moderately to severely active RA defined as the presence of at least 6/68 tender joints and at least 6/66 swollen joints. * Have a CRP (or hsCRP) measurement ≥ 6 mg/liter (L) based on the most recent data (if available). * Have had regular use of MTX for at least the 12 weeks prior to study entry at a dose that, in accordance with local clinical practice, is considered acceptable to adequately assess clinical response. The dose of MTX must have been a stable, unchanging oral dose of 7.5 to 25 mg/week (or the equivalent injectable dose) for at least the 8 weeks prior to study entry. The dose of MTX is expected to remain stable throughout the study and may be adjusted only for safety reasons. Exclusion Criteria: * Are currently receiving corticosteroids at doses \>10 mg of prednisone per day (or equivalent) or have been receiving an unstable dosing regimen of corticosteroids within 2 weeks of study entry or within 6 weeks of planned randomization. * Have started treatment with NSAIDs within 2 weeks of study entry or within 6 weeks of planned randomization or have been receiving an unstable dosing regimen of NSAIDs within 2 weeks of study entry or within 6 weeks of planned randomization. * Are currently receiving concomitant treatment with MTX, hydroxychloroquine, and sulfasalazine or combination of any 3 conventional disease modifying anti-rheumatic drugs (cDMARDs). * Are currently receiving or have received cDMARDs (for example, gold salts, cyclosporine, azathioprine, or any other immunosuppressives) other than MTX, hydroxychloroquine (up to 400 mg/day), or sulfasalazine (up to 3000 mg/day) within 8 weeks prior to study entry. * Have received leflunomide in the 12 weeks prior to study entry (or within 4 weeks prior to study entry if the standard 11 days of cholestyramine is used to washout leflunomide). * Have started a new physiotherapy treatment for RA in the 2 weeks prior to study entry. * Have ever received any biologic DMARD (such as tumor necrosis factor (TNF), interleukin-1, interleukin-6 (IL-6), or T-cell- or B-cell-targeted therapies). * Have received any parenteral corticosteroid administered by intramuscular or intravenous injection within 2 weeks prior to study entry or within 6 weeks prior to planned randomization or are anticipated to require parenteral injection of corticosteroids during the study. * Have had 3 or more joints injected with intraarticular corticosteroids or hyaluronic acid within 2 weeks prior to study entry or within 6 weeks prior to planned randomization. * Have a diagnosis of any systemic inflammatory condition other than RA such as, but not limited to, juvenile chronic arthritis, spondyloarthropathy, Crohn's disease, ulcerative colitis, psoriatic arthritis, active vasculitis or gout. * Have an estimated glomerular filtration rate (eGFR) based on the most recent available serum creatinine using the Modification of Diet in Renal Disease (MDRD) method of \<40 milliliters/minute/1.73 meters squared (m\^2). * Have a history of chronic liver disease with the most recent available aspartate aminotransferase (AST) or alanine aminotransferase (ALT) \>1.5 times the upper limit of normal (ULN) or the most recent available total bilirubin 1.5 times the ULN. * Have a current or recent (\<30 days prior to study entry) clinically serious viral, bacterial, fungal, or parasitic infection. * Have a history of active hepatitis B virus (HBV), hepatitis C virus (HCV), or human immunodeficiency virus (HIV). * Have had household contact with a person with active tuberculosis (TB) and did not receive appropriate and documented prophylaxis for TB. * Have evidence of active TB or have previously had evidence of active TB and did not receive appropriate and documented treatment. * Are pregnant or nursing at the time of study entry. * Are females of childbearing potential who do not agree to use 2 forms of highly effective birth control when engaging in intercourse while enrolled in the study and for at least 28 days following the last dose of orally administered investigational product. * Are males who do not agree to use 2 forms of highly effective birth control while engaging in sexual intercourse with female partners of childbearing potential while enrolled in the study and for at least 28 days following the last dose of orally administered investigational product. * Have previously been randomized in this study or any other study investigating baricitinib. * Have received prior treatment with an oral janus kinase inhibitor.