We combine Hubble Space Telescope (HST)/Wide Field Camera3 (WFC3) imaging and G141 grism observations from the Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey (CANDELS) and 3D-HST surveys to produce a catalog of grism spectroscopic redshifts for galaxies in the CANDELS/GOODS-South field. The WFC3/G141 grism spectra cover a wavelength range of 1.1 <= lambda <= 1.7 mu m with a resolving power of R similar to 130 for point sources, thus providing rest-frame optical spectra for galaxies out to z similar to 3.5. The catalog is selected in the H-band (F160W) and includes both galaxies with and without previously published spectroscopic redshifts. Grism spectra are extracted for all H-band detected galaxies with H <= 24 and a CANDELS photometric redshift z(phot) >= 0.6. The resulting spectra are visually inspected to identify emission lines, and redshifts are determined using cross-correlation with empirical spectral templates. To establish the accuracy of our redshifts, we compare our results against high-quality spectroscopic redshifts from the literature. Using a sample of 411 control galaxies, this analysis yields a precision of sigma(NMAD) = 0.0028 for the grism-derived redshifts, which is consistent with the accuracy reported by the 3D-HST team. Our final catalog covers an area of 153 arcmin(2) and contains 1019 redshifts for galaxies in GOODS-S. Roughly 60% (608/1019) of these redshifts are for galaxies with no previously published spectroscopic redshift. These new redshifts span a range of 0.677 <= z <= 3.456 and have a median redshift of z = 1.282. The catalog contains a total of 234 new redshifts for galaxies at z > 1.5. In addition, we present 20 galaxy pair candidates identified for the first time using the grism redshifts in our catalog, including four new galaxy pairs at z similar to 2, nearly doubling the number of such pairs previously identified.