Compact groups (CGs) of galaxies -- relatively poor groups of galaxies in which the typical separations between members is of the order of a galaxy diameter -- offer an exceptional laboratory for the study of dense galaxian environments with short (<1Gyr) dynamical time-scales. In this paper, we present an objectively defined catalog of CGs in 153 sq deg of the Sloan Digital Sky Survey Early Data Release (SDSS EDR). To identify CGs, we applied a modified version of Hickson's (1982) criteria aimed at finding the highest density CGs and thus reducing the number of chance alignments. Our catalog contains 175 CGs down to a limiting galaxy magnitude of r* = 21. The resulting catalog has a median depth of approximately z = 0.13, substantially deeper than previous CG catalogs. Since the SDSS will eventually image up to one quarter of the celestial sphere, we expect our final catalog, based upon the completed SDSS, will contain on the order of 5,000 - 10,000 CGs. This catalog will be useful for conducting studies of the general characteristics of CGs, their environments, and their component galaxies.