Study to Evaluate the Safety, Tolerability, PDs, and Efficacy of CNP-104 in Subjects With Primary Biliary Cholangitis

Inclusion Criteria: 1. Subjects who are willing and able to provide Institutional Review Board (IRB) approved written informed consent and privacy language as per national regulations. 2. Men and non-pregnant women, ages 18-75 years inclusive. 3. Subjects with a PBC diagnosis as demonstrated by the presence of 2 or more of the following 3 diagnostic factors: 1. Alkaline phosphatase \> 1.5× ULN for at least 6 months 2. Positive AMA titer or, if AMA negative or in low titer (\<1:40), positive PBC-specific antibodies (anti-GP210 and/or anti-SP100 and/or antibodies against the major M2 components \[PDC-E2, 2-oxo-glutaric acid dehydrogenase complex\]) 3. Liver biopsy findings consistent with PBC 4. Subjects who are unresponsive to UDCA and/or OCA after 6 months of treatment at a stable dose as measured by ALP \> 1.5× ULN. 5. For subjects on any medication used to treat the symptoms of PBC (ex. UDCA, OCA, seladelpar), subjects must be on a stable dose for a minimum of 3 months prior to enrollment and must agree not to change their dose through study Day 60 unless reviewed by the medical monitor and approved by the site investigator. 6. Subjects with ALP \> 1.5× ULN. 7. Subjects with AST and ALT \< 5× ULN. 8. Subjects with hemoglobin ≥ 10 g/dL. 9. Subjects with total bilirubin \< 2× ULN. 10. Men and women of child-bearing potential (WOCBP) must agree to practice a highly effective method of contraception that may include, but is not limited to, abstinence, sex only with persons of the same sex, monogamous relationship with vasectomized partner, vasectomy, hysterectomy, bilateral tubal ligation, licensed hormonal methods, intrauterine device (IUD) beginning at the time of screening through Day 90. 11. Female subjects who agree not to donate ova starting at initial screening and through Day 90. 12. Male subjects who agree to not donate sperm starting at screening and through Day 90. Exclusion Criteria: 1. Subjects with a Class B or Class C Child-Pugh score. 2. Subjects with concomitant liver diseases including chronic viral hepatitis B or C, autoimmune hepatitis, PSC, alcoholic liver disease, Wilson's disease, hemochromatosis, or Gilbert's syndrome. 3. Subjects who have previously undergone liver transplantation. 4. Subjects with decompensated liver disease as defined by the presence or history of any of the following: * MELD score \> 15 * Hepatic encephalopathy * Ascites * Hepatorenal syndrome or serum creatinine \> 2 mg/dL * Total Bilirubin \> 3.0 mg/dL * INR \>1.8 unless on anticoagulation such as Coumadin * History of variceal hemorrhage 5. Subjects with a history of cerebrovascular accident in the past 12 months. 6. Subjects with history of myocardial infarction, as defined by any of the following criteria: * Development of pathological Q waves with or without symptoms * Imaging evidence of a region of loss of viable myocardium that is thinned and fails to contract, in the absence of a non-ischemic cause * Pathological findings of a healed or healing myocardial 7. Subjects with chronic kidney disease, as defined by estimated glomerular filtration rate (eGFR) \< 60 mL/min/1.73 m2 for at least 3 months (per CKD EPI Equation - 2021). 8. Subjects with uncontrolled diabetes, as defined by HbA1c \> 7%. 9. Subjects who have used the following medications: * Methotrexate within 90 days of screening. * Immunotherapy drugs unless approved by the medical monitor. 10. Subjects with a history of tuberculosis or positive PPD skin test. 11. Subjects who have received administration of any live vaccine (other than intranasal Influenza) within 28 days or subunit vaccine within 14 days prior to screening or are planning to receive any vaccination before Day 90. 12. Subjects who have used systemic steroids within 3 months prior to screening. 13. Subjects with laboratory test results at screening or prior to study dosing that are outside the normal limits and considered by the Investigator to be clinically significant. Note: This criterion does not apply to liver function tests. Additionally, clinically significant laboratory test results at screening that are related to the condition (PBC) are acceptable as long as all inclusion and no other exclusion criteria are met. 14. Subjects with positive test results for hepatitis B surface antigen (HBsAg), hepatitis C virus (HCV) antibody, or human immunodeficiency virus (HIV) antigen/antibody as determined at screening. 15. Subjects with a history of or currently active immune disorders other that PBC (including autoimmune disease) unless the condition, after discussion with the Medical Monitor, has been deemed to be acceptable for the subject's participation in this study. 16. Subjects with a history of or current active diseases requiring immunosuppressive drugs (including azathioprine, prednisone, prednisolone, budesonide, cyclosporine, tacrolimus, methotrexate, or mycophenolate mofetil) unless the condition, after discussion with the Medical Monitor, has been deemed to be acceptable for the subject's participation in this study. 17. Subjects with a clinical history of significant cardiovascular disease as determined by the Investigator. 18. Subjects with a complication or medical history of malignancy within past 5 years which, in the Investigator's opinion, makes the subject unsuitable for study participation. 19. Subjects who, in the Investigator's opinion, will be unable to adhere to study procedures. 20. Subjects who have received an investigational therapy other than CNP-104 within 28 days or 5 half-lives, whichever is longer, prior to screening. 21. Subjects with any condition which, in the Investigator's opinion, makes the subject unsuitable for study participation. 22. Known sensitivity to any components of CNP-104.