Lyα forest absorption spectra toward quasars at z ~ 6 show regions of enhanced transmission close to their source. Several authors have argued that the apparently small sizes of these regions indicate that quasar ionization fronts at z 6 expand into a largely or partly neutral IGM. Assuming that the typical region in the IGM is reionized by z ≤ 6, as is suggested by Lyα forest observations, we argue that at least 50% of the volume of the IGM was reionized before the highest redshift quasars turned on. Further, even if the IGM is as much as ~50% neutral at quasar turn-on, the quasars are likely born into large galaxy-generated H II regions. The H II regions during reionization are themselves clustered, and using radiative transfer simulations, we find that long skewers through the IGM toward quasar progenitor halos pass entirely through ionized bubbles, even when the IGM is half-neutral. These effects have been neglected in most previous analyses of quasar proximity zones, which assumed a spatially uniform neutral fraction. We model the subsequent ionization from a quasar and construct mock Lyα forest spectra. Our mock absorption spectra are more sensitive to the level of small-scale structure in the IGM than to the volume-averaged neutral fraction and suggest that existing proximity zone size measurements are compatible with a fully ionized IGM. However, we mention several improvements in our modeling that are necessary to make more definitive conclusions.