Most patients with hepatocellular carcinoma (HCC) are diagnosed with advanced disease not eligible for potentially curative therapies; therefore, new treatment options are needed. Combining nivolumab with ipilimumab may improve clinical outcomes compared with nivolumab monotherapy. To assess efficacy and safety of nivolumab plus ipilimumab in patients with advanced HCC who were previously treated with sorafenib. CheckMate 040 is a multicenter, open-label, multicohort, phase 1/2 study. In the nivolumab plus ipilimumab cohort, patients were randomized between January 4 and September 26, 2016. Treatment group information was blinded after randomization. Median follow-up was 30.7 months. Data cutoff for this analysis was January 2019. Patients were recruited at 31 centers in 10 countries/territories in Asia, Europe, and North America. Eligible patients had advanced HCC (with/without hepatitis B or C) previously treated with sorafenib. A total of 148 patients were randomized (50 to arm A and 49 each to arms B and C). Patients were randomized 1:1:1 to either nivolumab 1 mg/kg plus ipilimumab 3 mg/kg, administered every 3 weeks (4 doses), followed by nivolumab 240 mg every 2 weeks (arm A); nivolumab 3 mg/kg plus ipilimumab 1 mg/kg, administered every 3 weeks (4 doses), followed by nivolumab 240 mg every 2 weeks (arm B); or nivolumab 3 mg/kg every 2 weeks plus ipilimumab 1 mg/kg every 6 weeks (arm C). Coprimary end points were safety, tolerability, and objective response rate. Duration of response was also measured (investigator assessed with the Response Evaluation Criteria in Solid Tumors v1.1). Of 148 total participants, 120 were male (81%). Median (IQR) age was 60 (52.5-66.5). At data cutoff (January 2019), the median follow-up was 30.7 months (IQR, 29.9-34.7). Investigator-assessed objective response rate was 32% (95% CI, 20%-47%) in arm A, 27% (95% CI, 15%-41%) in arm B, and 29% (95% CI, 17%-43%) in arm C. Median (range) duration of response was not reached (8.3-33.7+) in arm A and was 15.2 months (4.2-29.9+) in arm B and 21.7 months (2.8-32.7+) in arm C. Any-grade treatment-related adverse events were reported in 46 of 49 patients (94%) in arm A, 35 of 49 patients (71%) in arm B, and 38 of 48 patients (79%) in arm C; there was 1 treatment-related death (arm A; grade 5 pneumonitis). In this randomized clinical trial, nivolumab plus ipilimumab had manageable safety, promising objective response rate, and durable responses. The arm A regimen (4 doses nivolumab 1 mg/kg plus ipilimumab 3 mg/kg every 3 weeks then nivolumab 240 mg every 2 weeks) received accelerated approval in the US based on the results of this study. ClinicalTrials.gov Identifier: NCT01658878.