We present an optically selected catalog of 1073 galaxy cluster and group candidates at 0.3<~z<~1. These candidates are drawn from the Las Campanas Distant Clusters Survey (LCDCS), a drift-scan imaging survey of a 130 square degree strip of the southern sky. The survey data were obtained in 1995 March under photometric conditions using the Las Campanas 1 m telescope, the Great Circle Camera, and the Tek No. 5 CCD. To construct this catalog we utilize a novel detection process in which clusters are detected as positive surface brightness fluctuations in the background sky. This approach permits us to find clusters with significantly shallower data than other matched-filter methods that are based upon number counts of resolved galaxies. Selection criteria for the survey are fully automated so that this sample constitutes a well-defined, homogeneous sample that can be used to address issues of cluster evolution and cosmology. Estimated redshifts are derived for the entire sample, and an observed correlation between surface brightness and velocity dispersion, {sigma}, is used to estimate the limiting velocity dispersion of the survey as a function of redshift.