The questions of how planets form and how common Earth-like planets are can be addressed by measuring the distribution of exoplanet masses and orbital periods. We report the occurrence rate of close-in planets (with orbital periods less than 50 days), based on precise Doppler measurements of 166 Sun-like stars. We measured increasing planet occurrence with decreasing planet mass (M). Extrapolation of a power-law mass distribution fitted to our measurements, df/dlogM = 0.39 M-0.48, predicts that 23% of stars harbor a close-in Earth-mass planet (ranging from 0.5 to 2.0 Earth masses). Theoretical models of planet formation predict a deficit of planets in the domain from 5 to 30 Earth masses and with orbital periods less than 50 days. This region of parameter space is in fact well populated, implying that such models need substantial revision.