A star forms when a cloud of dust and gas collapses. It is generally believed that this collapse first produces a flattened rotating disk(1,2), through which matter is fed onto the embryonic star at the centre of the disk. When the temperature and density at the centre of the star pass a critical threshold, thermonuclear fusion begins. The remaining disk, which can still contain up to 0.3 times the mass of the star(3-5), is then sculpted and eventually dissipated by the radiation and wind from the newborn star. But this picture of the structure and evolution of the disk remains speculative because of the lack of morphological data of sufficient resolution and uncertainties regarding the underlying physical processes. Here we present images of a young star, LkH alpha 101, in which the structure of the inner accretion disk is resolved. We rnd that the disk is almost face-on, with a central gap (or cavity) and a hot inner edge. The cavity is bigger than previous theoretical predictions(6), and we infer that the position of the inner edge is probably determined by sublimation of dust grains by direct stellar radiation, rather than by disk-reprocessing or viscous-heating processes as usually assumed(29).