BACKGROUND: Extraskeletal myxoid chondrosarcoma is a rare sarcoma with low sensitivity to cytotoxic chemotherapy. Retrospective evidence suggests that antiangiogenic drugs could be a treatment option. We aimed to investigate the activity of pazopanib, an antiangiogenic drug, in patients with advanced extraskeletal myxoid chondrosarcoma. METHODS: In this single-arm, open-label phase 2 trial, three parallel independent cohorts of different histotypes of advanced sarcomas were recruited (extraskeletal myxoid chondrosarcoma, typical solitary fibrous tumour, and malignant-dedifferentiated solitary fibrous tumour). In each cohort, patients received pazopanib. In this Article, we report the results of the cohort of patients with advanced extraskeletal myxoid chondrosarcoma. Separate reporting of the three cohorts was prespecified in the study protocol. In this cohort, adult patients (aged ≥18 years) with a diagnosis of NR4A3-translocated, metastatic, or unresectable extraskeletal myxoid chondrosarcoma, who had Response Evaluation Criteria in Solid Tumors (RECIST) progression in the previous 6 months, and had an Eastern Cooperative Oncology Group performance status of 0-2, were enrolled at 11 study sites of the Spanish, Italian, and French sarcoma groups. Patients received oral pazopanib (800 mg/day) continuously, until disease progression, unacceptable toxicity, death, non-compliance, patient refusal, or investigator's decision. The primary endpoint was the proportion of patients achieving an objective response according to RECIST 1·1 in the modified intention-to-treat population (patients who provided consent and had a central molecularly confirmed diagnosis of extraskeletal myxoid chondrosarcoma). The safety analysis included all patients who received at least one dose of pazopanib. This study is registered with ClinicalTrials.gov, number NCT02066285. FINDINGS: Between June 24, 2014, and Jan 17, 2017, 26 patients entered the study and started pazopanib. Of these, 23 met the eligibility criteria for the modified intention-to-treat analysis. Median follow-up was 27 months (IQR 18-30). 22 patients (one patient died before the primary analysis) were evaluable for the primary endpoint: four (18% [95% CI 1-36]) had a RECIST objective response. No deaths or grade 4 adverse events occurred. The most frequent grade 3 adverse events were hypertension (nine [35%] of 26 patients), increased concentration of alanine aminotransferase (six [23%]), and increased aspartate aminotransferase (five [19%]). INTERPRETATION: Pazopanib had clinically meaningful antitumour activity in patients with progressive and advanced extraskeletal myxoid chondrosarcoma, and could be considered a suitable option after failure to respond to first-line anthracycline-based chemotherapy in these patients. FUNDING: Spanish Group for Research on Sarcomas, Italian Sarcoma Group, French Sarcoma Group, GlaxoSmithKline, and Novartis.