Background: There is a strong unmet need to improve systemic therapy in mesothelioma. Chemotherapy with cisplatin and pemetrexed improves survival in malignant pleural mesothelioma, and immune checkpoint inhibitors are an emerging treatment in this disease. We aimed to evaluate the activity of durvalumab, an anti-PD-L1 antibody, given during and after first-line chemotherapy with cisplatin and pemetrexed in patients with advanced malignant pleural mesothelioma. Methods: DREAM was a multicentre, single-arm, open-label, phase 2 trial done in nine hospitals in Australia. Eligible patients were aged 18 years or older and had histologically confirmed malignant pleural mesothelioma considered unsuitable for cancer-directed surgery, an Eastern Cooperative Oncology Group performance status of 0 or 1, and measurable disease as per the modified Response Evaluation Criteria in Solid Tumors version 1.0 (mRECIST) for mesothelioma that was previously untreated with systemic therapy. All histological subtypes were eligible. The first six participants were treated for two cycles in a safety run-in. All participants received cisplatin 75 mg/m2, pemetrexed 500 mg/m2, and durvalumab 1125 mg intravenously on day 1 of a 3-weekly schedule for a maximum of six cycles. Change from cisplatin to carboplatin with an area under the curve of 5 was permitted. Durvalumab was continued for a maximum of 12 months. The primary endpoint was progression-free survival at 6 months, measured according to mRECIST for malignant pleural mesothelioma and analysed in the intention-to-treat population. Safety analyses included all participants who receive at least one dose of any study drug. This study is registered with the Australia New Zealand Clinical Trials Registry, ACTRN12616001170415. Findings: Between Dec 28, 2016, and Sept 27, 2017, 55 participants were enrolled. 54 patients were eligible and were followed up for a median of 28·2 months (IQR 26·5–30·2). 31 (57%; 95% CI 44–70) of 54 patients were alive and progression-free at 6 months. The most common grade 3–4 adverse events were neutropenia (seven [13%] patients), nausea (six [11%]), and anaemia (four [7%]). A total of 60 serious adverse events occurred in 29 participants, five of which were considered possibly related to durvalumab. Five patients died during the study treatment; none of these five deaths were attributed to study treatment. Interpretation: The combination of durvalumab, cisplatin, and pemetrexed has promising activity and an acceptable safety profile that warrants further investigation in a randomised phase 3 trial. Funding: AstraZeneca.