Very large collisions in the asteroid belt could lead temporarily to a substantial increase in the rate of impacts of meteorites on Earth. Orbital simulations predict that fragments from such events may arrive considerably faster than the typical transit times of meteorites falling today, because in some large impacts part of the debris is transferred directly into a resonant orbit with Jupiter. Such an efficient meteorite delivery track, however, has not been verified. Here we report high-sensitivity measurements of noble gases produced by cosmic rays in chromite grains from a unique suite of fossil meteorites preserved in ~480 million year old sediments. The transfer times deduced from the noble gases are as short as ~105 years, and they increase with stratigraphic height in agreement with the estimated duration of sedimentation. These data provide powerful evidence that this unusual meteorite occurrence was the result of a long-lasting rain of meteorites following the destruction of an asteroid, and show that at least one strong resonance in the main asteroid belt can deliver material into the inner Solar System within the short timescales suggested by dynamical models.