Pulsars are rotating, magnetized neutron stars that are born in supernova explosions following the collapse of the cores of massive stars. If some of the explosion ejecta fails to escape, it may fall back onto the neutron star or it may possess sufficient angular momentum to form a disk. Such `fallback' is both a general prediction of current supernova models and, if the material pushes the neutron star over its stability limit, a possible mode of black hole formation. Fallback disks could dramatically affect the early evolution of pulsars, yet there are few observational constraints on whether significant fallback occurs or even the actual existence of such disks. Here we report the discovery of mid-infrared emission from a cool disk around an isolated young X-ray pulsar. The disk does not power the pulsar's X-ray emission but is passively illuminated by these X-rays. The estimated mass of the disk is of the order of 10 Earth masses, and its lifetime (>= 106years) significantly exceeds the spin-down age of the pulsar, supporting a supernova fallback origin. The disk resembles protoplanetary disks seen around ordinary young stars, suggesting the possibility of planet formation around young neutron stars.