We present the extensive and well-characterized Chandra X-ray Galaxy Catalog (CGC) of 8547 galaxy candidates in the redshift range z~0.04-0.07, optical luminosity 10^10^-10^11^L_r{sun}_, and X-ray luminosity (0.5-7keV) L_X_=2x10^40^-2x10^43^erg/s. We estimate a ~5% false-match fraction and contamination by quasi-stellar objects (QSOs). The CGC was extracted from the Chandra Source Catalog version-2 (CSC2) by cross-correlating with optical and IR all-sky survey data, including the Sloan Digital Sky Survey, Pan-STARRS, DESI Legacy, and Wide-field Infrared Survey Explorer (WISE). Our selection makes use of two main criteria that we have tested on the subsample with optical spectroscopical identification. (1) A joint selection based on X-ray luminosity (L_X_) and X-ray-to-optical flux ratio (F_XO_), which recovers 63% of the spectroscopically classified galaxies with a small contamination fraction (7%), which is a significant improvement over methods using L_X_ or F_XO_ alone (<50% recovery). (2) A joint W1-W2 (W_12_) WISE color and L_X_ selection that proves effective in excluding QSOs and improves our selection by recovering 72% of the spectroscopically classified galaxies and reducing the contamination fraction (4%). Of the CGC, 24% was selected by means of optical spectroscopy; 30% on the basis of L_X_, F_XO_, and W_12_; and 46% by using either the L_X_-F_XO_ or the L_X_-W_12_ selection criteria. We have individually examined the data for galaxies with z<0.1, which may include more than one CSC2 X-ray source, leading to the exclusion of 110 local galaxies. Our catalog also includes near-IR and UV data and galaxy morphological types.