From R-band images of 39 Hickson compact groups (HCGs), we use galaxy counts to determine a luminosity function. We find that a single Schechter function is a poor fit to the data, so we use a composite function consisting of separate Schechter functions for the bright and faint galaxies. The decreasing bright end slope implies a deficit of intermediate luminosity galaxies in our sample and the faint end is slightly steeper than that reported for earlier HCG luminosity functions. Furthermore, luminosity functions of subsets of our sample reveal more substantial dwarf populations for groups with X-ray halos, groups with tidal dwarf candidates, and groups with a dominant elliptical or lenticular galaxy. Collectively, these results support the hypothesis that within compact groups, the initial dwarf galaxy population is replenished by “subsequent generations” formed in the tidal debris of giant galaxy interactions.