The purpose of this study is to determine the safety and effectiveness of an experimental drug called K-808 in participants with primary biliary cholangitis (PBC). K-808 (also called K-877-ER or pemafibrate) is designed to slow down the worsening of PBC and help improve disease symptoms. The medication is also expected to lower the level of a liver enzyme, alkaline phosphatase, in the blood. K-808 works by joining onto a protein found in the body’s cells and may also reduce inflammation. Participants will be randomly assigned to 1 of 4 groups. The first group will receive placebo (inactive substance) for 12 weeks, then K-808 at .02 mg for 52 weeks. The second group will receive placebo for 12 weeks, then K-808 at .04 mg for 52 weeks. The third group will receive K-808 at .02 mg for 12 weeks, then continue with K-808 at .02 mg for 52 weeks. The fourth group will receive K-808 at .04 mg for 12 weeks, then continue with K-808 at .04 mg for 52 weeks. Participants will also be asked to complete blood draws, electrocardiograms, imaging (such as liver ultrasounds), urine collections, and fasting.