Only a few solar-type main sequence stars are known to be orbited by warm dust particles; the most extreme is the G0 field star BD+20 307 that emits ~4% of its energy at mid-infrared wavelengths. We report the identification of a similarly dusty star HD 23514, an F6-type member of the Pleiades cluster. A strong mid-IR silicate emission feature indicates the presence of small warm dust particles, but with the primary flux density peak at the non-standard wavelength of ~9 micron. The existence of so much dust within an AU or so of these stars is not easily accounted for given the very brief lifetime in orbit of small particles. The apparent absence of very hot (>~1000 K) dust at both stars suggests the possible presence of a planet closer to the stars than the dust. The observed frequency of the BD+20 307/HD 23514 phenomenon indicates that the mass equivalent of Earths Moon must be converted, via collisions of massive bodies, to tiny dust particles that find their way to the terrestrial planet zone during the first few hundred million years of the life of many (most?) sun-like stars. Identification of these two dusty systems among youthful nearby solar-type stars suggests that terrestrial planet formation is common.