The main purpose of this study is to learn more about the safety of LY3114062 and to find out how well it is tolerated in participants with an inflammatory arthritis. The study will also investigate how the body processes the drug and how the drug affects inflammatory arthritis. The study is expected to last about 3 months.

Inclusion Criteria:

• Signs or symptoms of an inflammatory arthritis for a duration of at least 8 weeks at screening.
• Presence of at least 3 out of 66 swollen joints at screening and baseline, as determined by the swollen joint count assessment forms.

Exclusion Criteria:

• Synthetic disease-modifying antirheumatic drugs DMARD use as follows:

  • ANY treatment with tofacitinib within 28 days prior to baseline or planned treatment with tofacitinib during the study;
  • Treatment with other synthetic DMARDs (eg, hydroxychloroquine, methothrexate, leflunomide, sulfasalazine, and gold salts) at an unstable dose within 28 days prior to baseline or if the dose of drug is planned to be changed during the study.

• Previous treatment with marketed biologic DMARDs as follows:

  • Etanercept, adalimumab, or anakinra <4 weeks prior to baseline;
  • Infliximab, certolizumab pegol, golimumab, abatacept, or tocilizumab <8 weeks prior to baseline;
  • Rituximab <12 months prior to baseline

Note: Other biologic agents for indications other than an inflammatory arthritis may be allowed after discussion with the sponsor

• Treatment with >10 mg/day, or unstable dose, of oral prednisone or equivalent within 28 days prior to baseline.
• Confirmed or suspected septic arthritis, crystal arthropathy, systemic lupus erythematosus, reactive arthritis, or certain other rheumatic conditions.