The infrared excess around the white dwarf G29-38 can be explained by emission from an opaque flat ring of dust with an inner radius of 0.14 R-. and an outer radius of less than 1 R-.. This ring lies within the Roche region of the white dwarf where an asteroid could have been tidally destroyed, producing a system reminiscent of Saturn's rings. Accretion onto the white dwarf from this circumstellar dust can explain the observed calcium abundance in the atmosphere of G29-38. Either as a bombardment by a series of asteroids or because of one large disruption, the total amount of matter accreted onto the white dwarf may have been similar to4 x 10(24) g, comparable to the total mass of asteroids in the solar system, or, equivalently, about 1% of the mass in the asteroid belt around the main-sequence star zeta Lep.