The extragalactic high-energy γ-ray sky is dominated by blazars, which are active galactic nuclei with their jets pointing towards us. Distance measurements are of fundamental importance yet for some of these sources are challenging because any spectral signature from the host galaxy may be outshone by the non-thermal emission from the jet. In this paper, we present a method to constrain redshifts for these sources that relies only on data from the Large Area Telescope on board the Fermi Gamma-ray Space Telescope. This method takes advantage of the signatures that the pair-production interaction between photons with energies larger than approximately 10 GeV and the extragalactic background light leaves on γ-ray spectra. We find upper limits for the distances of 303 γ-ray blazars, classified as 157 BL Lacertae objects, 145 of uncertain class, and 1 flat-spectrum-radio quasar, whose redshifts are otherwise unknown. These derivations can be useful for planning observations with imaging atmospheric Cherenkov telescopes and also for testing theories of supermassive black hole evolution. Our results are applied to estimate the detectability of these blazars with the future Cherenkov Telescope Array, finding that at least 21 of them could be studied in a reasonable exposure of 20 h.