Background: Poly (ADP-ribose) polymerase inhibitors combined with immunotherapy have shown antitumour activity in preclinical studies. We aimed to assess the safety and activity of olaparib in combination with the PD-L1-inhibitor, durvalumab, in patients with germline BRCA1-mutated or BRCA2-mutated metastatic breast cancer. Methods: The MEDIOLA trial is a multicentre, open-label, phase 1/2, basket trial of durvalumab and olaparib in solid tumours. Patients were enrolled into four initial cohorts: germline BRCA-mutated, metastatic breast cancer; germline BRCA-mutated, metastatic ovarian cancer; metastatic gastric cancer; and relapsed small-cell lung cancer. Here, we report on the cohort of patients with breast cancer. Patients who were aged 18 years or older (or aged 19 years or older in South Korea) with germline BRCA1-mutated or BRCA2-mutated or both and histologically confirmed, progressive, HER2-negative, metastatic breast cancer were enrolled from 14 health centres in the UK, the USA, Israel, France, Switzerland, and South Korea. Patients should not have received more than two previous lines of chemotherapy for metastatic breast cancer. Patients received 300 mg olaparib in tablet form orally twice daily for 4 weeks and thereafter a combination of olaparib 300 mg twice daily and durvalumab 1·5 g via intravenous infusion every 4 weeks until disease progression. Primary endpoints were safety and tolerability, and 12-week disease control rate. Safety was analysed in patients who received at least one dose of study treatment, and activity analyses were done in the full-analysis set (patients who received at least one dose of study treatment and were not excluded from the study). Recruitment has completed and the study is ongoing. This trial is registered with ClinicalTrials.gov, NCT02734004. Findings: Between June 14, 2016, and May 2, 2017, 34 patients were enrolled and received both study drugs and were included in the safety analysis. 11 (32%) patients experienced grade 3 or worse adverse events, of which the most common were anaemia (four [12%]), neutropenia (three [9%]), and pancreatitis (two [6%]). Three (9%) patients discontinued due to adverse events and four (12%) patients experienced a total of six serious adverse events. There were no treatment-related deaths. 24 (80%; 90% CI 64·3–90·9) of 30 patients eligible for activity analysis had disease control at 12 weeks. Interpretation: Combination of olaparib and durvalumab showed promising antitumour activity and safety similar to that previously observed in olaparib and durvalumab monotherapy studies. Further research in a randomised setting is needed to determine predictors of therapeutic benefit and whether addition of durvalumab improves long-term clinical outcomes compared with olaparib monotherapy. Funding: AstraZeneca.