Summary Background Rimegepant is a calcitonin gene-related peptide receptor antagonist that has shown efficacy and safety in the acute treatment of migraine. We aimed to compare the efficacy of rimegepant with placebo for preventive treatment of migraine. Methods We did a multicentre, phase 2/3, randomised, double-blind, placebo-controlled trial at 92 sites in the USA. Adults with at least a 1-year history of migraine were recruited. After a 4-week observation period, eligible participants were randomised using an interactive web response system to oral rimegepant 75 mg or matching placebo every other day for 12 weeks (double-blind treatment phase). The primary efficacy endpoint was change from the 4-week observation period in the mean number of migraine days per month in the last 4 weeks of the double-blind treatment phase (weeks 9–12). Participants who received at least one dose of their assigned study medication and who had 14 days or more of data in the observation period and 14 days or more of data for at least one 4-week interval during the double-blind treatment phase were analysed for efficacy. Those who received at least one dose of study medication were analysed for safety. This study is registered with ClinicalTrials.gov, NCT03732638. Findings Between Nov 14, 2018, and Aug 30, 2019, 1591 participants were recruited and assessed for eligibility, of whom 747 were randomly allocated either rimegepant (n=373) or placebo (n=374). 695 participants were included in the analysis for efficacy, of whom 348 were assigned rimegepant and 347 were allocated placebo. Rimegepant was superior to placebo on the primary endpoint of change in the mean number of migraine days per month during weeks 9–12. The change from the observation period in mean number of migraine days per month during weeks 9–12 was −4·3 days (95% CI –4·8 to –3·9) with rimegepant and −3·5 days (–4·0 to –3·0) with placebo (least squares mean difference −0·8 days, 95% CI −1·46 to −0·20; p=0·0099). 741 participants received study medication and were included in the safety analysis. 133 (36%) of 370 patients who received rimegepant reported an adverse event, compared with 133 (36%) of 371 who received placebo. Seven (2%) participants who received rimegepant and four (1%) who received placebo discontinued the study due to an adverse event; no patients died. Interpretation Taken every other day, rimegepant was effective for preventive treatment of migraine. Tolerability was similar to that of placebo, and no unexpected or serious safety issues were noted. Funding Biohaven Pharmaceuticals.