THE presence of dust around normal (main-sequence) Stars is a possible signature of the early stages of planet formation. Scattered light from the star beta Pictoris provides evidence of a dust disk extending out to about 1,000 astronomical units(1), and the observation of far-infrared excess emission from several other main-sequence stars(2) suggests the presence of orbiting cold dust grains(3). Because the dynamical lifetime of this dust is short, it is thought to be supplied and replenished by collisions among a population of comets or asteroids(4-8). Observations by Chini et al.(9,10) of beta Pic and several other infrared-excess stars at a wavelength of 1.3 mm have supported the idea that they are surrounded by extended dust disks. Techniques developed recently now permit imaging at these wavelengths, and we have used these techniques to obtain a map of the dust disk around the nearby, prototypical infrared-excess star Fomalhaut with a spatial resolution of 80 AU. This image provides direct confirmation that the dust is distributed it. a disk-like structure, and shows that the structure extends about 200 AU from the star, farther than estimated previously(9,10). We estimate that a high rate of cometary and/or asteroidal collisions is required to maintain this disk.