The peculiar object P/2010 A2 was discovered by the LINEAR near-Earth asteroid survey in January 2010 and given a cometary designation due to the presence of a trail of material, although there was no central condensation or coma. The appearance of this object, in an asteroidal orbit (small eccentricity and inclination) in the inner main asteroid belt attracted attention as a potential new member of the recently recognized class of 'Main Belt Comets' (MBCs). If confirmed, this new object would greatly expand the range in heliocentric distance over which MBCs are found. Here we present observations taken from the unique viewing geometry provided by ESA's Rosetta spacecraft, far from the Earth, that demonstrate that the trail is due to a single event rather than a period of cometary activity, in agreement with independent results from the Hubble Space Telescope (HST). The trail is made up of relatively large particles of millimetre to centimetre size that remain close to the parent asteroid. The shape of the trail can be explained by an initial impact ejecting large clumps of debris that disintegrated and dispersed almost immediately. We determine that this was an asteroid collision that occurred around February 10, 2009. ; Comment: Published in Nature on 14/10/2010. 25 pages, includes supplementary material