For the first time, we construct a catalog of compact groups selected from a complete, magnitude-limited redshift survey. We select groups with $N \geq 3$ members based on projected separation and association in redshift space alone. We evaluate the characteristics of the Redshift Survey Compact Groups (RSCG's). Their physical properties (membership frequency, velocity dispersion, density) are similar to those of the Hickson [ApJ, 255, 382 (1982)] Compact Groups. Hickson's isolation criterion is a strong function of the physical and angular group radii and is a poor predictor of the group environment. In fact, most RSCG's are embedded in dense environments. The luminosity function for RSCG's is mildly inconsistent with the survey luminosity function --- the characteristic luminosity is brighter and the faint end shallower for the RSCG galaxies. We construct a model of the selection function of compact groups. Using this selection function, we estimate the abundance of RSCG's; for groups with $N \geq 4$ members the abundance is $3.8 \times 10^{-5} h^3 Mpc^{-3}$. For all RSCG's ($N \geq 3$) the abundance is $1.4 \times 10^{-4} h^3 Mpc^{-3}$.

41 pages, LaTeX, including 20 figures and 9 tables. Accepted for publication in The Astronomical Journal. Figures 3 and 4 available at ftp://cfa0.harvard.edu/outgoing/barton