We carry out an independent search of Kepler photometry for small transiting planets with sizes 0.5-8.0 times that Earth and orbital periods between 5 and 50 days, with the goal of measuring the fraction of stars harboring such planets. We use a new transit search algorithm, TERRA, optimized to detect small planets around photometrically quiet stars. We restrict our stellar sample to include the 12,000 stars having the lowest photometric noise in the Kepler survey, thereby maximizing the detectability of Earth-size planets. We report 129 planet candidates having radii less than 6 RsubE found in three years of Kepler photometry. We compute the occurrence of planets as a function of planet radius and period, correcting for the detection completeness as well as the geometric probability of transit, R/a. The occurrence of planets is consistent with constant from 2 RsubE toward 1 RsubE. This unexpected plateau in planet occurrence at 2 RsubE suggests distinct planet formation processes for planets above and below 2 RsubE.