We present accurate photometric redshifts for galaxies observed by the Cluster Lensing and Supernova survey with Hubble (CLASH). CLASH observed 25 massive galaxy cluster cores with the Hubble Space Telescope in 16 filters spanning 0.2 - 1.7 $mu$m. Photometry in such crowded fields is challenging. Compared to our previously released catalogs, we make several improvements to the photometry, including smaller apertures, ICL subtraction, PSF matching, and empirically measured uncertainties. We further improve the Bayesian Photometric Redshift (BPZ) estimates by adding a redder elliptical template and by inflating the photometric uncertainties of the brightest galaxies. The resulting photometric redshift accuracies are dz/(1+z) $sim$ 0.8%, 1.0%, and 2.0% for galaxies with I-band F814W AB magnitudes $<$ 18, 20, and 23, respectively. These results are consistent with our expectations. They improve on our previously reported accuracies by a factor of 4 at the bright end and a factor of 2 at the faint end. Our new catalog includes 1257 spectroscopic redshifts, including 382 confirmed cluster members. We also provide stellar mass estimates. Finally, we include lensing magnification estimates of background galaxies based on our public lens models. Our new catalog of all 25 CLASH clusters is available via MAST. The analysis techniques developed here will be useful in other surveys of crowded fields, including the Frontier Fields and surveys carried out with J-PAS and JWST.
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