The transit method, employed by Microvariability and Oscillation of Stars (MOST), Kepler, and various ground-based surveys has enabled the characterization of extrasolar planets to unprecedented precision. These results are precise enough to begin to measure planet atmosphere composition, planetary oblateness, starspots, and other phenomena at the level of a few hundred parts per million. However, these results depend on our understanding of stellar limb darkening, that is, the intensity distribution across the stellar disk that is sequentially blocked as the planet transits. Typically, stellar limb darkening is assumed to be a simple parameterization with two coefficients that are derived from stellar atmosphere models or fit directly. In this work, we revisit this assumption and compute synthetic planetary-transit light curves directly from model stellar atmosphere center-to-limb intensity variations (CLIVs) using the plane-parallel Atlas and spherically symmetric SAtlas codes. We compare these light curves to those constructed using best-fit limb-darkening parameterizations. We find that adopting parametric stellar limb-darkening laws leads to systematic differences from the more geometrically realistic model stellar atmosphere CLIV of about 50–100 ppm at the transit center and up to 300 ppm at ingress/egress. While these errors are small, they are systematic, and they appear to limit the precision necessary to measure secondary effects. Our results may also have a significant impact on transit spectra.