A Study of Baricitinib (LY3009104) in Participants With Primary Biliary Cholangitis Who do Not Respond or Cannot Take UDCA

Inclusion Criteria: * Have a diagnosis of PBC (consistent with American Association for the Study of Liver Disease (AASLD) and European Association for Study of the Liver (EASL) Practice Guidelines; as demonstrated by the presence of at least 2 of the following 3 diagnostic factors: * History of elevated Alkaline Phosphatase (ALP) levels for at least 6 months * Positive antimitochondrial antibodies titer * Liver biopsy consistent with PBC * Have ALP ≥1.67 x ULN but ≤6 x Upper Limit Normal (ULN). * Taking UDCA for at least 52 weeks (stable dose for at least 12 weeks) prior to Week 0, or have previously taken, but are intolerant (in the opinion of the investigator) to UDCA and have not received UDCA for at least 12 weeks prior to Week 0. * Nonpregnant, nonbreastfeeding female participants of childbearing potential. Exclusion Criteria: * History or presence of other concomitant liver diseases including: * Hepatitis C virus (HCV) infection * Hepatitis B virus (HBV) infection * Primary sclerosing cholangitis * Alcoholic liver disease * Autoimmune liver disease other than PBC, such as overlap hepatitis * Nonalcoholic steatohepatitis * Gilbert's syndrome * Presence of clinical complications of PBC or clinically significant hepatic decompensation, including: * Liver transplantation, current placement on a liver transplant list or current Model for End Stage Liver Disease (MELD) score ≥15 * Portal hypertension with complications, including known gastric or esophageal varices, ascites, history of variceal bleeds or related therapeutic or prophylactic interventions (e.g., beta blockers, insertion of variceal bands or transjugular intrahepatic portosystemic shunt), or hepatic encephalopathy * Cirrhosis, including history or presence of one or more of the following: * spontaneous bacterial peritonitis * hepatocellular carcinoma * Hepatorenal syndrome (type I or II) * Have an estimated glomerular filtration rate (eGFR) based on the most recent available serum creatinine of \<90 milliliters/minute/1.73 m2. * Have screening electrocardiogram (ECG) abnormalities that in the opinion of the investigator or the sponsor are clinically significant and indicate an unacceptable risk for the participant's participation in the study. * Have experienced any of the following within 12 weeks of screening: myocardial infarction, unstable ischemic heart disease, stroke, or New York Heart Association Stage III/IV heart failure. * Have a history of venous thromboembolism (VTE) (deep vein thrombosis/pulmonary embolism \[DVT/PE\]). * Have a history or presence of cardiovascular, respiratory, hepatic, gastrointestinal, endocrine, hematological, neurological, or neuropsychiatric disorders or any other serious and/or unstable illness that, in the opinion of the investigator, could constitute an unacceptable risk when taking investigational product or interfere with the interpretation of data. * Have a current or recent (\<4 weeks prior to randomization) clinically serious infection or any other active or recent infection that, in the opinion of the investigator, would pose an unacceptable risk to the participant if participating in the study. * Have had symptomatic herpes zoster infection within 12 weeks prior to randomization. * Have active tuberculosis (TB) disease determined on the basis of a positive medical history, physical examination, or chest radiography (per local standard of care) or latent TB infection (LTBI). * Have any of the following specific abnormalities based on screening central lab test results: * Hemoglobin \<10 grams per deciliter (100.0 grams per liter) * Alanine aminotransferase (ALT) \>3 x ULN * aspartate aminotransferase (AST) \>3 x ULN * alkaline phosphatase (ALP) \>6 x ULN * Total bilirubin level (TBL) \>ULN * Creatine phosphokinase (CPK) \> ULN * Serum albumin \< lower limit of normal (LLN) * International Normalized Ratio of Prothrombin Time (INR) \> ULN * Total white blood cell (WBC) count \<LLN * Absolute neutrophil count (ANC) \<LLN * Lymphocyte count \<LLN * Platelet (thrombocyte) count \<LLN * Are receiving unstable treatment for pruritus within 6 weeks prior to Week 0. * Have been treated with systemic (oral or parenteral) corticosteroids within 6 weeks prior to Week 0. * Have received biologic treatments for an immunologic disease within 4 weeks of screening. * Have received a Janus kinase (JAK) inhibitor. * Have received obeticholic acid. * Have received fenofibrate or other fibrates for the treatment of PBC.