Background: Approved systemic treatments for malignant pleural mesothelioma (MPM) have been limited to chemotherapy regimens that have moderate survival benefit with poor outcomes. Nivolumab plus ipilimumab has shown clinical benefit in other tumour types, including first-line non-small-cell lung cancer. We hypothesised that this regimen would improve overall survival in MPM. Methods: This open-label, randomised, phase 3 study (CheckMate 743) was run at 103 hospitals across 21 countries. Eligible individuals were aged 18 years and older, with previously untreated, histologically confirmed unresectable MPM, and an Eastern Cooperative Oncology Group performance status of 0 or 1. Eligible participants were randomly assigned (1:1) to nivolumab (3 mg/kg intravenously once every 2 weeks) plus ipilimumab (1 mg/kg intravenously once every 6 weeks) for up to 2 years, or platinum plus pemetrexed chemotherapy (pemetrexed [500 mg/m2 intravenously] plus cisplatin [75 mg/m2 intravenously] or carboplatin [area under the concentration-time curve 5 mg/mL per min intravenously]) once every 3 weeks for up to six cycles. The primary endpoint was overall survival among all participants randomly assigned to treatment, and safety was assessed in all participants who received at least one dose of study treatment. This study is registered with ClinicalTrials.gov, NCT02899299, and is closed to accrual. Findings: Between Nov 29, 2016, and April 28, 2018, 713 patients were enrolled, of whom 605 were randomly assigned to either nivolumab plus ipilimumab (n=303) or chemotherapy (n=302). 467 (77%) of 605 participants were male and median age was 69 years (IQR 64–75). At the prespecified interim analysis (database lock April 3, 2020; median follow-up of 29·7 months [IQR 26·7–32·9]), nivolumab plus ipilimumab significantly extended overall survival versus chemotherapy (median overall survival 18·1 months [95% CI 16·8–21·4] vs 14·1 months [12·4–16·2]; hazard ratio 0·74 [96·6% CI 0·60–0·91]; p=0·0020). 2-year overall survival rates were 41% (95% CI 35·1–46·5) in the nivolumab plus ipilimumab group and 27% (21·9–32·4) in the chemotherapy group. Grade 3–4 treatment-related adverse events were reported in 91 (30%) of 300 patients treated with nivolumab plus ipilimumab and 91 (32%) of 284 treated with chemotherapy. Three (1%) treatment-related deaths occurred in the nivolumab plus ipilimumab group (pneumonitis, encephalitis, and heart failure) and one (<1%) in the chemotherapy group (myelosuppression). Interpretation: Nivolumab plus ipilimumab provided significant and clinically meaningful improvements in overall survival versus standard-of-care chemotherapy, supporting the use of this first-in-class regimen that has been approved in the USA as of October, 2020, for previously untreated unresectable MPM. Funding: Bristol Myers Squibb.