Background: Most patients with small-cell lung cancer (SCLC) have extensive-stage disease at presentation, and prognosis remains poor. Recently, immunotherapy has demonstrated clinical activity in extensive-stage SCLC (ES-SCLC). The CASPIAN trial assessed durvalumab, with or without tremelimumab, in combination with etoposide plus either cisplatin or carboplatin (platinum–etoposide) in treatment-naive patients with ES-SCLC. Methods: This randomised, open-label, phase 3 trial was done at 209 sites across 23 countries. Eligible patients were adults with untreated ES-SCLC, with WHO performance status 0 or 1 and measurable disease as per Response Evaluation Criteria in Solid Tumors, version 1.1. Patients were randomly assigned (in a 1:1:1 ratio) to durvalumab plus platinum–etoposide; durvalumab plus tremelimumab plus platinum–etoposide; or platinum–etoposide alone. All drugs were administered intravenously. Platinum–etoposide consisted of etoposide 80–100 mg/m2 on days 1–3 of each cycle with investigator's choice of either carboplatin area under the curve 5–6 mg/mL per min or cisplatin 75–80 mg/m2 (administered on day 1 of each cycle). Patients received up to four cycles of platinum–etoposide plus durvalumab 1500 mg with or without tremelimumab 75 mg every 3 weeks followed by maintenance durvalumab 1500 mg every 4 weeks in the immunotherapy groups and up to six cycles of platinum–etoposide every 3 weeks plus prophylactic cranial irradiation (investigator's discretion) in the platinum–etoposide group. The primary endpoint was overall survival in the intention-to-treat population. We report results for the durvalumab plus platinum–etoposide group versus the platinum–etoposide group from a planned interim analysis. Safety was assessed in all patients who received at least one dose of their assigned study treatment. This study is registered at ClinicalTrials.gov, NCT03043872, and is ongoing. Findings: Patients were enrolled between March 27, 2017, and May 29, 2018. 268 patients were allocated to the durvalumab plus platinum–etoposide group and 269 to the platinum–etoposide group. Durvalumab plus platinum–etoposide was associated with a significant improvement in overall survival, with a hazard ratio of 0·73 (95% CI 0·59–0·91; p=0·0047]); median overall survival was 13·0 months (95% CI 11·5–14·8) in the durvalumab plus platinum–etoposide group versus 10·3 months (9·3–11·2) in the platinum–etoposide group, with 34% (26·9–41·0) versus 25% (18·4–31·6) of patients alive at 18 months. Any-cause adverse events of grade 3 or 4 occurred in 163 (62%) of 265 treated patients in the durvalumab plus platinum–etoposide group and 166 (62%) of 266 in the platinum–etoposide group; adverse events leading to death occurred in 13 (5%) and 15 (6%) patients. Interpretation: First-line durvalumab plus platinum–etoposide significantly improved overall survival in patients with ES-SCLC versus a clinically relevant control group. Safety findings were consistent with the known safety profiles of all drugs received. Funding: AstraZeneca.