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 transam…