Previous studies have concluded that the Sun is a typical star as regards its chemical composition, but our elemental abundance analysis of unprecedented accuracy shows that the Sun is not a typical Sun-like star. The Sun shows a characteristic signature of dust condensation with a ~20% depletion of refractory elements relative to the volatile elements in comparison with most solar-type stars, including all stars in our study known to have close-in giant planets. The abundance differences correlate strongly with the condensation temperatures for the elements. We propose that the differences in abundance patterns are related to the formation of terrestrial planets. Thus our technique can be used to select the best targets for discovering terrestrial planets like our own Earth.