Direct observational searches for Population III (Pop III) stars at high redshift are faced with the question of how to select the most promising targets for spectroscopic follow-up. To help answer this, we use a large-scale cosmological simulation, augmented with a new subgrid model that tracks the fraction of pristine gas, to follow the evolution of high-redshift galaxies and the Pop III stars they contain. We generate rest-frame ultraviolet (UV) luminosity functions for our galaxies and find that they are consistent with current z ≥ 7 observations. Throughout the redshift range 7 ≤ z ≤ 15 we identify "Pop III-bright" galaxies as those with at least 75% of their flux coming from Pop III stars. While less than 1% of galaxies brighter than m UV,AB = 31.4 mag are Pop III-bright in the range 7 ≤ z ≤ 8, roughly 17% of such galaxies are Pop III-bright at z = 9, immediately before reionization occurs in our simulation. Moving to z = 10, m UV,AB = 31.4 mag corresponds to larger, more luminous galaxies and the Pop III-bright fraction falls off to 5%. Finally, at the highest redshifts, a large fraction (29% at z = 14 and 41% at z = 15) of all galaxies are Pop III-bright regardless of magnitude. While m UV,AB = 31.4 mag galaxies are extremely rare during this epoch, we find that 13% of galaxies at z = 14 are Pop III-bright with m UV,AB ≤ 33 mag, an intrisic magnitude within reach of the James Webb Space Telescope using lensing. Thus, we predict that the best redshift to search for luminous Pop III-bright galaxies is just before reionization, while lensing surveys for fainter galaxies should push to the highest redshifts possible.