• Known diagnosis of histologically-confirmed BE with either no dysplasia, indefinite for dysplasia, or low-grade dysplasia as defined by the presence of specialized columnar epithelium on histology and \>= 2 cm of involvement on endoscopy

• Adequate Barrett's mucosa, which is defined as at least one sample with \>= 50% intestinal metaplasia in biopsies required to satisfy the endpoints of the study

• Participants are on proton pump inhibitors (PPI) therapy for \>= 28 days duration

• Age \>= of 18 years. Because no dosing or adverse event (AE) data are currently available on the use of OCA in participants \< 18 years of age, children are excluded from this study but will be eligible for future pediatric trials, if applicable

• Eastern Cooperative Oncology Group (ECOG) performance status =\< 1 (Karnofsky \>= 70%)

• Hemoglobin \>= 10g/dL or hematocrit \>= 30 %

• Leukocyte count \>= 3,500/microliter

• Platelet count \>= 100,000/microliter

• Creatinine clearance (calculated if measured is not available) \>= 30mL/min/1.73m\^2

• Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 1.5 X institutional upper limit of normal (ULN)

• Total bilirubin =\< 1.0 X ULN

• Alkaline phosphatase =\<1.5 X ULN

• Gamma-glutamyl transferase (GGT) =\< 1.5 X ULN

• The effects of OCA on the developing human fetus are unknown. For this reason, all men and women of child-bearing potential must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry, throughout the duration of study participation, and for at least 6 months after receiving the last dose of study drug. Should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her study physician immediately

• Ability to understand the study procedures, benefits and risks, and sign a written informed consent document. Non-English speaking participants are allowed to enroll even if they skip answering quality-of-life (QOL) questionnaires. Special efforts will be made through community advisory boards at participating sites to reach Spanish speaking participants

• Willing to undergo testing for human immunodeficiency virus (HIV) testing if not tested within the past 6 months

• Willing to undergo hepatitis B and C screening if not tested within the past 6 months

• Willing and able to adhere to the prohibitions and restrictions specified in the approved protocol

• Willingness to moderate alcohol intake (consuming no more than 1 or 2 alcoholic drinks per day for women and men, respectively)

• Participants must have no evidence of active or recurrent invasive cancer for 6 months prior to screening and must be at least 6 months from any prior cancer-directed treatment (such as surgical resection, chemotherapy, immunotherapy, hormonal therapy or radiation)