A Study in Participants With Rheumatoid Arthritis on Background Methotrexate Therapy

The purpose of this trial is to evaluate the safety and efficacy of LY3009104 in participants with Rheumatoid Arthritis (RA).

This study consists of the following:

* Screening period: 4 to 28-days
* Part A: a 12-week blinded, placebo controlled treatment period
* Part B: a 12-week blinded extension period
* Part C: an optional 52-week open-label extension period
* Part D: an additional optional 52-week open-label extension period
* Follow up period: 28 days

Eligibility Criteria:
Inclusion Criteria:

* Must have active RA
* Must regularly use methotrexate (MTX) for at least 12 weeks before your participation in this study
* Must have American College of Rheumatology (ACR) functional class I, II, or III
* Must have C-reactive protein (CRP) measurement \> 1.2 times upper limit of normal (ULN) or Erythrocyte Sedimentation Rate (ESR) \> ULN \[28 millimeters/hour (mm/hr)\]
* Have laboratory values that in the opinion of the investigator do not pose an unacceptable risk to the participants if study drug would be administered
* Must have venous access sufficient to allow blood sampling as per the protocol
* Must be reliable and willing to be available for the duration of the study and are willing to follow study procedures
* Must be able to read, understand, and give written informed consent approved by Lilly or its designee and the ethical review board (ERB) governing the site
* Male participants: agree to use 2 forms of highly effective methods of birth control with female partners of childbearing potential during the study
* If you are a woman and you could become pregnant during this study, you must talk to the study doctor about birth control. You are required to use 2 forms of highly effective methods of birth control to avoid getting pregnant during the study
* If you are a post-menopausal woman, you must be at least 45 years of age and have not menstruated for the last 12 months
* If you are a woman between 40 and 45 years of age, test negative for pregnancy, and have not menstruated during the last 12 months only, you must have an additional blood test
* For participants receiving corticosteroids, you must be on a dose not to exceed 10 mg of prednisone daily (or equivalent) and have been on the same dosing regimen for at least 6 weeks prior to randomization
* Continue to meet inclusion criteria for Parts A and B as applicable
* Part D only: have completed the 52 weeks (Week 24 to Week 76) of participation in Part C of the study without permanent study drug discontinuation and have not completed the Follow-Up Visit (approximately 28 days after the last dose of study drug)

Exclusion Criteria:

* Must not have received any parenteral corticosteroid administered by intra-articular, intramuscular (IM), or intravenous (IV) injection within 6 weeks prior to baseline
* Must not be concomitantly using non-steroidal anti-inflammatory drugs (NSAIDS), unless you are on a stable dose within the last 4 weeks
* Must not have received any prior biologic disease modifying anti-rheumatic drug (DMARD) therapy \[such as Tumor necrosis factor-alpha (TNFα), interleukin (IL)-1, IL-6, T-cell or B-cell target therapies)
* Must not have used DMARDs other than methotrexate (MTX), hydroxychloroquine, or sulfasalazine within the last 8 weeks
* Must not have used leflunomide within the last 12 weeks and have not received cholestyramine to speed up the elimination of leflunomide from your body
* Must not have previously been randomized, completed or withdrawn from this study or any other study investigating LY3009104
* Must not have received prior treatment with an oral JAK inhibitor
* Must not have a current or recent (within the last 30 days) viral, bacterial, fungal, or parasitic infection
* Must not have had a serious infection (for example, pneumonia, cellulitis, or bone or joint infections) or atypical mycobacterial infection within the last 6 months
* Must not have had symptomatic herpes zoster or herpes simplex infection within the last 90 days or have a history of disseminated/complicated herpes zoster
* Must not have evidence of human immunodeficiency virus (HIV) and/or positive human HIV antibodies
* Must not have evidence of hepatitis C virus (HCV) or active hepatitis B
* Must not have evidence or suspicion of active or latent tuberculosis (TB)
* Must not have another serious disorder or illness
* Must not be exposed to a live vaccine within the last 12 weeks
* Must not have donated more than 500 milliliters (mL) of blood within the last month
* Must not have had surgery on a joint that is to be assessed in the study within the last 2 months, or will require such during the study
* Must not be currently enrolled in, or discontinued within the last 30 days from a clinical trial involving an investigational drug or device or off-label use of a drug, or concurrently enrolled in any other type of medical research judged not to be scientifically or medically compatible with this study
* Presence of significant uncontrolled cerebro-cardiovascular \[for example (eg), myocardial infarction (MI), unstable angina (UA), unstable arterial hypertension, severe heart failure or cerebrovascular accident\], respiratory, hepatic, renal, gastrointestinal (GI), endocrine, hematologic or neuropsychiatric disorders, or abnormal laboratory values that in the opinion of the investigator pose an unacceptable risk to the participant if study drug would be administered