The slow but persistent collisions between asteroids in our Solar System generate a tenuous cloud of dust known as the zodiacal light (because of the light the dust reflects). In the young Solar System, such collisions were more common and the dust production rate should have been many times larger. Yet copious dust in the zodiacal region around stars much younger than the Sun has rarely been found. Dust is known to orbit around several hundred main-sequence stars, but this dust is cold and comes from a Kuiper-belt analogous region out beyond the orbit of Neptune. Despite many searches, only a few main-sequence stars reveal warm (> 120K) dust analogous to zodiacal dust near the Earth. Signs of planet formation (in the form of collisions between bodies) in the regions of stars corresponding to the orbits of the terrestrial planets in our Solar System have therefore been elusive. Here we report an exceptionally large amount of warm, small, silicate dust particles around the solar-type star BD+20 307 (HIP8920, SAO75016). The composition and quantity of dust could be explained by recent frequent or huge collisions between asteroids or other `planetesimals' whose orbits are being perturbed by a nearby planet.