Since 1995, astronomers have discovered planets with masses comparable to that of Jupiter (318 times Earths mass) in orbit around approximately 60 stars. Although unseen directly, the presence of these planets is inferred by the small reflex motions that they gravitationally induce on the star they orbit; these result in small periodic wavelength shifts in the stellar spectrum. Since this method favors the detection of massive objects orbiting in close proximity to the star, the question of whether these systems also contain analogs of the smaller constituents of our Solar System has remained unanswered. Using an alternative approach, we report here observations of an aging carbon-star, IRC+10216, that reveal the presence of circumstellar water vapor, a molecule not expected in measurable abundances around such a star and thus a distinctive signature of an orbiting cometary system. The only plausible explanation for this water vapor is that the recent evolution of IRC+10216 - which is accompanied by a prodigious increase in its luminosity - is now causing the vaporization of a collection of orbiting icy bodies, a process first considered in a previous theoretical study.