The main purpose of this study is to find out how the body will react to a study drug called baricitinib when taken with another drug called omeprazole.

For each participant, this study will include 2 periods in fixed order. The study will last approximately 25 days, not including screening.

Inclusion Criteria:

• Overtly healthy as determined by medical history and physical examination
• Women not of childbearing potential due to surgical sterilization (at least 3 months after surgical hysterectomy, bilateral oophorectomy with or without hysterectomy, or bilateral tubal occlusion/ligation) confirmed by medical history, or menopause
• Have a body mass index of 18 to 29 kilograms per square meter (kg/m^2), inclusive, at screening

Exclusion Criteria:

• Have known allergies to baricitinib, omeprazole, related compounds, or any components of the baricitinib or omeprazole formulations, or history of significant atopy
• Have a history of or current cardiovascular, respiratory, hepatic, renal, gastrointestinal, endocrine, hematological (including clotting disorders), or neurological disorders capable of significantly altering the absorption, metabolism, or elimination of drugs; of constituting a risk when taking the study medication; or of interfering with the interpretation of data
• Have an absolute neutrophil count (ANC) less than 2 × 10^9 cells per liter (L) [2000 cells/microliter (μL)] at screening or Day -1. For abnormal values, a single repeat will be allowed
• Intend to use over-the-counter or prescription medication (including drugs and substances known to alter gastric potential hydrogen (pH), such as proton pump inhibitors or over-the-counter antacid remedies and/or herbal supplements within 14 days prior to dosing and during the study (with the exception of hormone replacement therapy (HRT) and occasional paracetamol, which will be permitted at the discretion of the investigator), or intended use of vitamin supplements from Day 1 until discharge from the clinical research unit (CRU)
• Have used or intend to use any drugs or substances that are known to be substrates, inhibitors, or inducers of cytochrome P450 3A4 (CYP3A4) within 30 days prior to dosing and throughout the study
• Are unable to tolerate or unwilling to undergo insertion of a nasogastric pH probe for assessment of gastric pH during the study

All enrolled participants.

Baseline through study completion (up to Day 24).