A Study to Evaluate Abemaciclib in Advanced Biliary Tract Carcinoma

Inclusion Criteria: 1. Male or female, age ≥ 18 years at the time of informed consent. 2. Capable and willing to sign informed consent form prior to performing any protocol-related procedures. 3. Histologic or cytologic evidence of advanced or metastatic biliary tract cancer, including cholangiocarcinoma (intra-hepatic or extra-hepatic bile ducts), ampullary carcinoma, or gallbladder carcinoma. 4. Evidence of recurrent, locally advanced, unresectable, or metastatic disease. 5. Progressed following or intolerant to one or more lines of systemic therapy, or treatment-naïve subjects who either decline or being considered not a good candidate first-line systemic chemotherapy per the opinion of the treating physician 6. Per the opinion of the physician investigator, predicted life expectancy \> 3 months. 7. Presence of at least 1 lesion that is measurable or evaluable using Response Evaluation Criteria in Solid Tumors (RECIST) v1.1. 8. Eastern Cooperative Oncology Group (ECOG) performance score of ≤ 2. 9. Per the opinion of the physician investigator, acute toxicities relating to any prior anticancer treatment have improved to Grade 1 or baseline. Exceptions include residual alopecia or Grade 2 peripheral neuropathy. 10. Ability to swallow capsules. 11. Adequate organ function as evidenced by the laboratory parameters noted in Section 3.0 Study Eligibility. 12. Women of childbearing potential (WOCP) defined as not surgically sterile (hysterectomy, tubal ligation, or oophorectomy), or at least 1 year postmenopausal, must have a negative serum pregnancy test before study drug administration on cycle 1 day 1. 13. WOCP must use a medically acceptable method of contraception and must agree to continue used of this method for the duration of the study and for 3 weeks after last dose of study drug. Acceptable methods of contraception include abstinence, barrier method with spermicide, intrauterine device (IUD) known to have a failure rate of less than 1% per year, or steroidal contraceptive (oral, transdermal, implanted, or injected) in conjunction with a barrier method. 14. Male, capable of producing offspring, must use a medical acceptable method of contraception and agree to continued use of this method for the duration of the study and for 3 weeks after last dose of study drug because of the possible effects on spermatogenesis. Acceptable methods of contraception include abstinence, WOCP partner's use of barrier method with spermicide, WOCP partner's use of an IUD known to have a failure rate of less than 1% per year, WOCP partner's use of steroidal contraceptive (oral, transdermal, implanted or injected) or WOCP partner is surgically sterile or at least 1 year post-menopausal. In addition, male subjects may not donate sperm for the duration of the study and for 30 days after last dose of study drug. 15. Must be willing and able to comply with the protocol, including adhering to study restrictions, remaining at the clinic as required during the study period, and willing to return to the clinic for the follow-up evaluation. 16. Patients who received chemotherapy must have recovered (Common Terminology Criteria for Adverse Events \[CTCAE\] Grade ≤1) from the acute effects of chemotherapy except for residual alopecia or Grade 2 peripheral neuropathy. 17. Patients who received radiotherapy must have completed and fully recovered from the acute effects of radiotherapy. A washout period of at least 14 days is required between end of radiotherapy and randomization. 18. Completed last dose of myelosuppressive chemotherapy greater than 21 days prior to first dose of study drug. 19. Completed last dose of non-myelosuppressive biological or monoclonal antibody therapy greater than 14 days prior to first dose of study drug. Exclusion Criteria: 1. Ongoing or active infection requiring systemic antibiotics. 2. Uncontrolled hypertension despite adequate therapy (systolic blood pressure higher than 150 mm Hg or diastolic blood pressure higher than 90 mm Hg found on 2 separate occasions separated by 1 week). 3. Diabetes mellitus and occurrence of more than 2 episodes of ketoacidosis in the 12 months prior to the first dose of study drug. 4. Active second malignancy other than curatively resected basal cell carcinoma of the skin, squamous cell carcinoma of the skin, in situ carcinoma of the cervix, or other cancers treated with curative intent, and no known active disease in the 3 years prior to enrollment. 5. Primary brain tumor or brain metastases from another primary site. 6. Known history of human immunodeficiency virus (HIV). 7. Known active viral hepatitis B or viral hepatitis C. 8. History of any of the following conditions: syncope of cardiovascular etiology, ventricular arrhythmia of pathological origin (including, but not limited to, ventricular tachycardia and ventricular fibrillation), or sudden cardiac arrest. Subjects with controlled atrial fibrillation for more than 30 days are permitted. 9. Congestive heart failure (New York Heart Association \[NYHA\] Class III or IV), or acute coronary syndromes within 6 months of enrollment. 10. Female subjects who are pregnant or breastfeeding. 11. Any other medical, psychiatric, or social condition, which in the opinion of the physician investigator, would preclude participation in the study, pose an undue medical hazard, interfere with the conduct of the study, or interfere with interpretation of the study results. For example, interstitial lung disease, severe dyspnea at rest or requiring oxygen therapy. 12. Use of an investigational drug within 1 month before the screening visit or currently participating in another investigational study. 13. Any disorder that may interfere with drug absorption, distribution, metabolism, or excretion (including extensive gastrointestinal surgery that involves removal of the entire stomach or most of the small intestine or large intestine, bariatric surgery, uncontrolled active Crohn's Disease or ulcerative colitis, or preexisting condition resulting in baseline Grade 2 or higher diarrhea). History of Whipple's procedure is permitted. 14. Known hypersensitivity to any of the components in abemaciclib including micro-crystalline cellulose 102, microcrystalline cellulose 101, lactose monohydrate, croscarmellose sodium, sodium stearyl fumarate, silicon dioxide. Color mixture ingredients-polyvinyl alcohol, titanium dioxide, polyethylene glycol, talc, iron oxide yellow, and iron oxide red. 15. The patient has serious and/or uncontrolled preexisting medical condition(s) that, in the judgment of the investigator, would preclude participation in this study (for example, interstitial lung disease, severe dyspnea at rest or requiring oxygen therapy, severe renal impairment \[e.g. estimated creatinine clearance \<30ml/min\].