A Study to Test the Safety and Feasibility of Nivolumab With Drug Eluting Bead Transarterial Chemoembolization in Patients With Liver Cancer

Inclusion Criteria: * Age 18 and over at the time of consent * Histology and/or cytology confirmed HCC per the enrolling institution. Subjects in Cohort 1 are permitted to enroll w ithout confirmation of HCC as long as imaging LiRADs criteria are met and a biopsy is scheduled prior to or the day of the deb-TACE procedure. HCC confirmation must be completed prior to initiation of nivolumab for all cohorts. If a patient is found to not have confirmed HCC, they w ill be removed from the study. * Measurable disease per RECIST v1.1 * Disease not amenable to curative or transplant surgery (BCLC Stage B); disease must be reviewed by members of disease management team at the local enrolling institution and be amenable to deb-TACE. For the dose escalation and the expansion, regional lymphadenopathy and sub-centimeter pulmonary nodules are allowed as well as segmental portal vein involvement. * ECOG Performance status 0 or 1 * Child-Pugh Class A * Child-Pugh Scoring Note: PI INR \<1.7 is not required for patients on anticoagulation agents. Patients who are being therapeutically anticoagulated with an agent such as Coumadin or heparin will be allowed to participate provided that no prior evidence of underlying abnormality in these parameters exists * Adequate bone marrow, hepatic, and renal function defined as: * Platelet count ≥ 75,000/mm3 * Absolute neutrophil count ≥ 1,000/mm3 * Hemoglobin ≥ 9 g/dL * Total bilirubin \< 3.0 × ULN (upper limit of normal) * Aspartate transaminase (AST) and alanine transaminase (ALT) ≤ 5 × ULN * Albumin ≥ 2.8 g/dL * Serum creatinine ≤ 1.5 mg/dL or calculated creatinine clearance ≥ 40 mL/min as determined by the Cockcroft-Gault equation * Suppression of HBV (≤ 100 IU/mL by HBV PCR) with antivirals per the local standard of care if prior or current HBV exposure or infection. * Active HCV infection without treatment is permitted. Concomitant treatment of HCV is not permitted on this study. Exclusion Criteria: * Vascular invasion or extrahepatic spread * History of liver allograft; prior hepatic resection is allowed. * Prior embolization and/or ablation is allowed as long as the patient has progressed with a new RECIST measurable lesion * Contraindication to angiography/embolization procedure based on judgment of the treating investigator. * Prior treatment with an anti-PD-1, anti-PD-L1, anti-PD-L2, anti-CTLA-4 antibody, or any other antibody or drug specifically targeting T-cell costimulation or immune checkpoint pathways * Known history of testing positive for human immunodeficiency virus (HIV) or known acquired immunodeficiency syndrome (AIDS) * A history of a severe contrast allergy (.i.e. anaphylaxis) not controlled with premedication * Patients should be excluded if they have a condition requiring chronic systemic treatment with either corticosteroids (\> 10 mg daily prednisone equivalents) or other immunosuppressive medications within 14 days of study drug administration. Inhaled or topical steroids and adrenal replacement doses \> 10 mg daily prednisone equivalents are permitted in the absence of active autoimmune disease. Patients with contrast allergies who can tolerate contrast with corticosteroid premedication are not excluded. * An active, known or suspected autoimmune disease. Subjects are permitted to enroll if they have vitiligo, type I diabetes mellitus, residual hypothyroidism due to autoimmune condition only requiring hormone replacement, psoriasis not requiring systemic treatment, or conditions not expected to recur in the absence of an external trigger. * Subjects with history of another primary cancer, with the exception of: a) curatively resected non-melanoma skin cancer; b) curatively treated cervical carcinoma in situ; or c) other primary solid tumor with no known active disease present that in the opinion of the investigator will not affect patient outcome in the setting of current HCC diagnosis. * Any condition that, in the opinion of the investigator, would interfere with evaluation of the investigational product or interpretation of subject safety or study results * Women of childbearing potential (WOCBP) or sexually active men must use appropriate method(s) of contraception. * Women of childbearing potential (WOCBP) must use appropriate method(s) of contraception while on study treatment. WOCBP should use an adequate method to avoid pregnancy during study treatment and for 5 months (30 days plus the time required for nivolumab to undergo five half-lives) after the last dose of investigational drug * Men who are sexually active with WOCBP must use any contraceptive method with a failure rate of less than 1% per year Men receiving nivolumab and who are sexually active with WOCBP will be instructed to adhere to contraception during study treatment and for a period of 7 months after the last dose of investigational product * Women who are not of childbearing potential (ie, who are postmenopausal or surgically sterile, as well as azoospermic men do not require contraception * Women of childbearing potential must have a negative serum or urine pregnancy test (minimum sensitivity 25 IU/L or equivalent units of HCG) within 24 hours prior to the start of nivolumab. Elevated HCG for other explained and documented reasons is allowed. * Lactating woman