Background: Rucaparib, a poly(ADP-ribose) polymerase inhibitor, has anticancer activity in recurrent ovarian carcinoma harbouring a BRCA mutation or high percentage of genome-wide loss of heterozygosity. In this trial we assessed rucaparib versus placebo after response to second-line or later platinum-based chemotherapy in patients with high-grade, recurrent, platinum-sensitive ovarian carcinoma. Methods: In this randomised, double-blind, placebo-controlled, phase 3 trial, we recruited patients from 87 hospitals and cancer centres across 11 countries. Eligible patients were aged 18 years or older, had a platinum-sensitive, high-grade serous or endometrioid ovarian, primary peritoneal, or fallopian tube carcinoma, had received at least two previous platinum-based chemotherapy regimens, had achieved complete or partial response to their last platinum-based regimen, had a cancer antigen 125 concentration of less than the upper limit of normal, had a performance status of 0-1, and had adequate organ function. Patients were ineligible if they had symptomatic or untreated central nervous system metastases, had received anticancer therapy 14 days or fewer before starting the study, or had received previous treatment with a poly(ADP-ribose) polymerase inhibitor. We randomly allocated patients 2:1 to receive oral rucaparib 600 mg twice daily or placebo in 28 day cycles using a computer-generated sequence (block size of six, stratified by homologous recombination repair gene mutation status, progression-free interval after the penultimate platinum-based regimen, and best response to the most recent platinum-based regimen). Patients, investigators, site staff, assessors, and the funder were masked to assignments. The primary outcome was investigator-assessed progression-free survival evaluated with use of an ordered step-down procedure for three nested cohorts: patients with BRCA mutations (carcinoma associated with deleterious germline or somatic BRCA mutations), patients with homologous recombination deficiencies (BRCA mutant or BRCA wild-type and high loss of heterozygosity), and the intention-to-treat population, assessed at screening and every 12 weeks thereafter. This trial is registered with ClinicalTrials.gov, number NCT01968213; enrolment is complete. Findings: Between April 7, 2014, and July 19, 2016, we randomly allocated 564 patients: 375 (66%) to rucaparib and 189 (34%) to placebo. Median progression-free survival in patients with a BRCA-mutant carcinoma was 16·6 months (95% CI 13·4-22·9; 130 [35%] patients) in the rucaparib group versus 5·4 months (3·4-6·7; 66 [35%] patients) in the placebo group (hazard ratio 0·23 [95% CI 0·16-0·34]; p<0·0001). In patients with a homologous recombination deficient carcinoma (236 [63%] vs 118 [62%]), it was 13·6 months (10·9-16·2) versus 5·4 months (5·1-5·6; 0·32 [0·24-0·42]; p<0·0001). In the intention-to-treat population, it was 10·8 months (8·3-11·4) versus 5·4 months (5·3-5·5; 0·36 [0·30-0·45]; p<0·0001). Treatment-emergent adverse events of grade 3 or higher in the safety population (372 [99%] patients in the rucaparib group vs 189 [100%] in the placebo group) were reported in 209 (56%) patients in the rucaparib group versus 28 (15%) in the placebo group, the most common of which were anaemia or decreased haemoglobin concentration (70 [19%] vs one [1%]) and increased alanine or aspartate aminotransferase concentration (39 [10%] vs none). Interpretation: Across all primary analysis groups, rucaparib significantly improved progression-free survival in patients with platinum-sensitive ovarian cancer who had achieved a response to platinum-based chemotherapy. ARIEL3 provides further evidence that use of a poly(ADP-ribose) polymerase inhibitor in the maintenance treatment setting versus placebo could be considered a new standard of care for women with platinum-sensitive ovarian cancer following a complete or partial response to second-line or later platinum-based chemotherapy. Funding: Clovis Oncology.