Using the powerful Earth-occultation technique, long-term, nearly continuous monitoring of the entire low-energy gamma-ray sky is now possible with the advent of BATSE, the Burst and Transient Source Experiment on board the Compton Gamma Ray Observatory (CGRO). In this paper, we present a catalog of 34 moderately strong gamma-ray sources measured by BATSE. It consists of 0.03 - 1.8 MeV photon spectra averaged over weeks and months, and light curves of the 35 - 200 keV flux, with 1 day resolution, covering the first three phases of the CGRO mission (1991 May through 1994 October). This database contains a complete record of {~}1200 daily source count rates in 14 energy channels along with the corresponding Poisson and systematic errors.