Inclusion Criteria:  Subjects who are willing and able to provide Institutional Review Board (IRB) approved written informed consent and privacy language as per national regulations. Men and non-pregnant women, ages 18-75 years inclusive.  Subjects with a confirmed diagnosis of Primary Biliary Cholangitis based upon at least two of the following:  AMA titer > 1:40 Alkaline phosphatase > 1.5× ULN for at least 6 months Liver biopsy findings consistent with PBC 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. Subjects positive for anti-mitochondrial antibodies (by QUANTA Lite® M2EP (MIT3) ELISA). Subjects with a Class A Child-Pugh score. Subjects with ALP > 1.5× ULN. Subjects with AST and ALT < 5× ULN. Female subjects of non-childbearing potential or women of child-bearing potential who have agreed not to become pregnant during the study, have a negative pregnancy test at both screening visits and prior to each dose and agree to use two highly effective forms of birth control starting at initial screening and continuing through Day 120. Female subjects who agree to not breastfeed starting at initial screening and through Day 120. Female subjects who agree to not donate ova starting at initial screening and through Day 120. Female subjects who are of childbearing potential and agree to use highly effective contraception consisting of two forms of birth control starting at initial screening and continuing through Day 120. Male subjects who agree to not donate sperm starting at screening and through Day 120.  Exclusion Criteria:  4.2 Exclusion Criteria  Subjects with greater than early Stage 3 Primary Biliary Cholangitis. Subjects with a Class B or Class C Child-Pugh score. Subjects with concomitant liver diseases including viral hepatitis, autoimmune hepatitis, PSC, alcoholic liver disease, Wilson's disease, hemochromatosis, or Gilbert's syndrome. Subjects who have previously undergone liver transplantation.  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 Subjects with a history of cerebrovascular accident.  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  Subjects with chronic kidney disease, as defined by by Glomerular Filtration Rate (GFR) < 60 mL/min/1.73 m2 for at least 3 months where GFR is calculated based on the CKD-EPI equation:  • GFR = 141 × min (Scr /κ, 1)α × max(Scr /κ, 1)-1.209 × 0.993Age × 1.018 [if female] × 1.159 [if black] where:  Scr is serum creatinine in mg/dL κ is 0.7 for females and 0.9 for males α is -0.329 for females and -0.411 for males Min indicates the minimum of Scr /κ or 1 Max indicates the maximum of Scr /κ or 1 Subjects with uncontrolled diabetes, as defined by HbA1c > 7%. Subjects who have used biologic agents including anti-cell and anti-cytokine therapies within 12 months of Day 0. Subjects with a history of tuberculosis or positive PPD skin test. Subjects who have received administration of any live vaccine (other than intranasal Influenza) within 28 days or subunit vaccine within 14 days prior to Screen 1 or are planning to receive any vaccination at any time during the study. Subjects who have received any COVID-19 vaccine (either first or second dose) within 14 days prior to Screening. Subjects who have received the first dose of any COVID-19 vaccine may not screen for the study until 14 days following their last dose of the vaccine if applicable. Subjects who have used systemic steroids within 3 months prior to screening. 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. 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. Subjects with a history of or currently active immune disorders other that PBC (including autoimmune disease) and/or diseases requiring immunosuppressive drugs (including azathioprine, prednisone, prednisolone, budesonide, cyclosporine, tacrolimus, methotrexate, or mycophenolate mofetil). Subjects with a clinical history of significant cardiovascular disease as determined by the Investigator. Subjects with a complication or medical history of malignancy. Subjects with a mental condition such as schizophrenia, bipolar disorder, any major depressive disorder, or subjects who have received drug(s) for the treatment of dementia. Subjects who have received an investigational therapy other than CNP-104 within 28 days or 5 half-lives, whichever is longer, prior to screening. Subjects with any condition which, in the investigator's opinion, makes the subject unsuitable for study participation. Known sensitivity to any components of CNP-104.