- Population III (Pop III) galaxies are predicted to exist at high redshifts and may be rendered sufficiently bright for detection with current telescopes when gravitationally lensed by a foreground galaxy cluster. Pop III galaxies that exhibit strong Lyα emission should furthermore be identifiable from broadband photometry because of their unusual colors. Here, we report on a search for such objects at z ≳ 6 in the imaging data from the Cluster Lensing And Supernova survey with Hubble (CLASH), covering 25 galaxy clusters in 16 filters. Our selection algorithm returns five singly imaged candidates with Lyα-like color signatures, for which ground-based spectroscopy with current 8–10 m class telescopes should be able to test the predicted strength of the Lyα line. None of these five objects have been included in previous CLASH compilations of high-redshift galaxy candidates. However, when large grids of spectral synthesis models are applied to the study of these objects, we find that only two of these candidates are significantly better fitted by Pop III models than by more mundane, low-metallicity stellar populations.