The Kuiper belt is a remnant of the primordial Solar System. Measurements of its size distribution constrain its accretion and collisional history, and the importance of material strength of Kuiper belt objects. Small, sub-kilometre-sized, Kuiper belt objects elude direct detection, but the signature of their occultations of background stars should be detectable. Observations at both optical and X-ray wavelengths claim to have detected such occultations, but their implied abundances are inconsistent with each other and far exceed theoretical expectations. Here we report an analysis of archival data that reveals an occultation by a body with an approximately 500-metre radius at a distance of 45 astronomical units. The probability of this event arising from random statistical fluctuations within our data set is about two per cent. Our survey yields a surface density of Kuiper belt objects with radii exceeding 250 metres of 2.1(-1.7)(+4.8) x 10(7) deg(-2), ruling out inferred surface densities from previous claimed detections by more than 5sigma. The detection of only one event reveals a deficit of sub-kilometre-sized Kuiper belt objects compared to a population extrapolated from objects with radii exceeding 50 kilometres. This implies that sub-kilometre-sized objects are undergoing collisional erosion, just like debris disks observed around other stars.