A growing body of evidence indicates that binary neutron-star mergers are the primary origin of heavy elements produced exclusively through rapid neutron capture1,2,3,4 (the ‘r-process’). As neutron-star mergers occur infrequently, their deposition of radioactive isotopes into the pre-solar nebula could have been dominated by a few nearby events. Although short-lived r-process isotopes—with half-lives shorter than 100 million years—are no longer present in the Solar System, their abundances in the early Solar System are known because their daughter products were preserved in high-temperature condensates found in meteorites5. Here we report that abundances of short-lived r-process isotopes in the early Solar System point to their origin in neutron-star mergers, and indicate substantial deposition by a single nearby merger event. By comparing numerical simulations with the early Solar System abundance ratios of actinides produced exclusively through the r-process, we constrain the rate of occurrence of their Galactic production sites to within about 1−100 per million years. This is consistent with observational estimates of neutron-star merger rates6,7,8, but rules out supernovae and stellar sources. We further find that there was probably a single nearby merger that produced much of the curium and a substantial fraction of the plutonium present in the early Solar System. Such an event may have occurred about 300 parsecs away from the pre-solar nebula, approximately 80 million years before the formation of the Solar System.