BACKGROUND: Malignant mesothelioma remains an incurable cancer, with no effective treatments in the setting of relapsed disease. Homologous recombination deficiency predicts sensitivity to poly (ADP-ribose) polymerase (PARP) inhibitors. In mesothelioma, BRCA1-associated protein 1 carboxy-terminal hydrolase (BAP1), which regulates DNA repair, is frequently mutated. We aimed to test the hypothesis that BAP1-deficient or BRCA1-deficient mesotheliomas would be sensitive to PARP inhibition by rucaparib. METHODS: We did a single-centre, open-label, single-arm, phase 2a trial in Leicester, UK, with prospective molecular stratification (Mesothelioma-Stratified Therapy 1 [MiST1]). Patients aged 18 years or older who had radiologically progressing, histologically confirmed, malignant mesothelioma after at least one course of systemic treatment; with cytoplasmic-BAP1-deficient or BRCA1-deficient mesothelioma (pleural or peritoneal or other primary localisation), and who met the other inclusion criteria, were deemed eligible. All eligible patients who consented to take part were given rucaparib 600 mg twice a day orally, for six cycles of 28 days, or until disease progression, unacceptable toxicity, withdrawal of consent, or death. Response was measured by CT scan every 6 weeks. The primary outcome was disease control (complete response, partial response, or stable disease) at 12 weeks in all patients who received study drug; secondary outcomes were the safety and toxicity profile, objective response rate (proportion of complete or partial responses), and disease control rate at 24 weeks. Recruitment is now closed. This trial is registered with ClinicalTrials.gov, NCT03654833. FINDINGS: Between Feb 9 and June 10, 2019, we enrolled 26 molecularly and clinically eligible patients. Ten (38%) of 26 patients were BAP1 negative and BRCA1 negative, 23 patients (89%) were BAP1 negative, and 13 patients (50%) were BRCA1 negative. Disease control rate at 12 weeks was 58% (95% CI 37-77; 15 of 26 patients), and at 24 weeks was 23% (9-44; six of 26 patients). Rucaparib was well tolerated, with 15 (9%) of 166 adverse events being grade 3 or 4, which were seen in nine (35%) of 26 patients, and there were no deaths. The most common grade 1-2 adverse events were nausea (18 [69%] of 26 patients), fatigue (14 patients [54%]), and decreased appetite (ten patients [38%]). The most common grade 3-4 adverse events were upper respiratory tract infection (three patients [12%]) and anaemia (three patients [12%]). All six cycles of rucaparib were received by eight (31%) of 26 patients. One or more dose reductions occurred in nine patients (35%). INTERPRETATION: Rucaparib in patients with BAP1-negative or BRCA1-negative mesothelioma met the prespecified criteria for success, showing promising activity with manageable toxicity. Further investigation of homologous recombination deficiency mutations is planned to refine the identification of predictive biomarkers for PARP inhibition in mesothelioma. FUNDING: University of Leicester (Leicester, UK), Asthma UK and British Lung Foundation Partnership, and the Victor Dahdaleh Foundation (Toronto, ON, Canada).