We present the deepest optical photometry for any dwarf elliptical (dE) galaxy based on Hubble Space Telescope ACS observations of the Local Group dE galaxies NGC 147 and NGC 185. The resulting F606W and F814W color-magnitude diagrams are the first to reach below the main sequence turnoff in a dE galaxy, allowing us to determine full star formation histories in these systems. The ACS fields are located ~1.5 effective radii from the galaxy center to avoid photometric crowding. While our ACS pointings in both dEs show unambiguous evidence for old and intermediate age stars, the mean age in NGC 147 is ~ 4 Gyr younger as compared to NGC 185. In NGC 147, only 40% of stars were in place 12.5 Gyrs ago (z~5), with the bulk of the remaining stellar population forming between 5 to 7 Gyr. In contrast, 70% of stars were formed in NGC 185 field more than12.5 Gyr ago with the majority of the remaining population forming between 8 to 10 Gyr. Star formation ceased in both ACS fields at least 3 Gyr ago. Previous observations in the central regions of NGC 185 show evidence for star formation as recent as 100 Myr ago and a strong metallicity gradient with radius. We suggest that the orbit of NGC 185 has a larger pericenter as compared to NGC 147, allowing it to preserve radial gradients and maintain a small central reservoir of recycled gas. We interpret the inferred differences in star formation histories to imply an earlier infall time into the M31 environment for NGC 185 as compared to NGC 147.