Study stopped due to poor accrual.

External beam photon stereotactic body radiotherapy (SBRT) using a linear accelerator to a total dose of 40 Gy in 5 fractions delivered once daily with at least 48 hours between each fraction. SBRT treatment will be completed within a 21-day window. Starting within 14 days after completion of SBRT, intravenous nivolumab 240 mg will be given every 2 weeks as monotherapy or in combination with ipilimumab 1 mg/kg IV every 6 weeks.

1.1 Primary Objective & Hypothesis Determine the safety and tolerability of SBRT followed by nivolumab or ipilimumab with nivolumab for hepatocellular carcinoma by establishing the rates of toxicity that occur within 6 months from start of SBRT. Hypothesis: SBRT followed by nivolumab or nivolumab and ipilimumab will have similar toxicity to historical controls of SBRT or nivolumab monotherapy.

1.2 Secondary Objectives and Hypotheses Estimate the investigator determined best overall response rate. Hypothesis: Combining radiation and nivolumab or nivolumab and ipilimumab will improve the best overall response rate compared to historical controls with SBRT or nivolumab alone.

Estimate the rates of long-term adverse events (after 6 months) from the end of SBRT. Hypothesis: Long-term toxicity from SBRT with nivolumab or nivolumab and ipilimumab will be comparable to that observed with nivolumab monotherapy.

Summarize the distant disease control, progression-free survival, and overall survival. Hypothesis: Disease control and survival will be comparable to (or better than) that observed with nivolumab monotherapy.

Summarize the local control of the SBRT treated lesion. Hypothesis: Combining SBRT and nivolumab or nivolumab and ipilimumab will have similar (or better) local control rates as observed in SBRT only series.

1.3 Exploratory Objectives Explore changes in inflammatory biomarkers (including, but not limited to CD8/Treg ratio, total CD4 counts, total lymphocyte count) in pretreatment and on-treatment serially collected peripheral blood samples. Hypothesis: Changes in inflammatory biomarkers after radiation therapy may correlate with a more favorable response to immunotherapy.

Explore changes in the tumor microenvironment induced by radiation on pre and post treatment biopsies. Hypothesis: Changes in the tumor microenvironment after radiation therapy will be observed that may correlate with a more favorable response to immunotherapy.

Inclusion Criteria:

• Be willing and able to provide written informed consent for the trial.
• Be ≥ 18 years of age on day of signing informed consent.
• Have ECOG performance status 0-1.
• Pretreatment CT chest /abdomen /pelvis within 28 days of protocol enrollment.
• Pathologic diagnosis of hepatocellular carcinoma (including fibrolamellar variants and biphenotypic tumors with an HCC component).
• Child Pugh Class A (score = 5 or 6)cirrhosis (assessed within 14 days of SBRT)
• Deemed ineligible for curative intent therapy with surgical resection or liver transplantation.
• Patients with diffuse/multifocal liver involvement are eligible.
• Patients with extrahepatic disease are eligible.
• Prior systemic therapies for HCC are allowed but not required.
• Must have at least one intrahepatic lesion amenable to SBRT.
• Prior transarterial chemoembolization (TACE) or radiofrequency ablation (RFA) allowed, however, patient must have separate intrahepatic lesion amenable to SBRT and biopsy.
• Intrahepatic lesion amenable to pre and post SBRT biopsies, unless the investigator determines that the tumor biopsies would be unsafe.
• Have measurable disease based on RECIST 1.1.
• Demonstrate adequate organ function as defined in Table 1. All screening labs should be performed within 14 days of treatment initiation.

Table 1 - Adequate Organ Function Laboratory Values System Laboratory Value Hematological Platelets ≥ 40,000 / mcL Hepatic Serum total bilirubin ≤ 3 mg/dL AST (SGOT) and ALT (SGPT) ≤ 5 X ULN

• Negative urine or serum pregnancy within 72 hours prior to receiving the first dose of study medication for female subjects of childbearing age.
• Subjects should agree to use an adequate method of contraception starting with the first dose of study therapy through 150 days after the last dose of study therapy (for women of child-bearing potential) or 210 days after the last dose of study therapy (for men who have partners of child-bearing potential).
• Have a life expectancy of greater than 6 months (in the opinion of the treating physician).

Exclusion Criteria:

• Prior external beam radiation therapy to the liver (defined as > 1 Gy).
• Prior yttrium-90 radioembolization treatment.
• Patients with HBV viral load > 100 IU/mL (antiviral therapy per local practice is required).
• Is currently participating and receiving study therapy or has participated in a study of an investigational agent and received study therapy or used an investigational device within 4 weeks of the first dose of treatment.
• Has a diagnosis of immunodeficiency or is receiving systemic steroid therapy at a dose of >10 mg prednisone daily or equivalent at time of first dose of trial treatment.
• Has a known history of active TB (Bacillus Tuberculosis).
• Hypersensitivity to nivolumab or ipilimumab or any of its excipients.
• Has had prior anticancer therapy within 4 weeks of study Day 1 or has not recovered (i.e., ≤ Grade 1 or at baseline) from adverse events due to agents administered more than 4 weeks earlier.
• Has a known additional malignancy that is progressing or requires active treatment.
• Has active autoimmune disease that has required systemic treatment in the past 2 years (i.e. with use of disease modifying agents, corticosteroids or immunosuppressive drugs). Replacement therapy (e.g., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency, etc.) is not considered a form of systemic treatment. Patients with allografts (including liver transplants) are not eligible for this protocol.
• Has known history of, or any evidence of active, non-infectious pneumonitis.
• Has an active infection requiring systemic therapy.
• Has a history or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the trial, interfere with the subject's participation for the full duration of the trial, or is not in the best interest of the subject to participate, in the opinion of the treating investigator.
• Has known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial.
• Is pregnant or breastfeeding, or expecting to conceive or father children within the projected duration of the trial, starting with the screening visit through 120 days after the last dose of trial treatment.
• Has received a live vaccine within 30 days of planned start of study therapy.
• Note: Seasonal influenza vaccines for injection are generally inactivated flu vaccines and are allowed; however intranasal influenza vaccines (e.g., Flu-Mist®) are live attenuated vaccines, and are not allowed.