As part of the HST/ACS Coma Cluster Treasury Survey, we have undertaken a Keck/LRIS spectroscopic campaign to determine membership for faint dwarf galaxies. In the process, we discovered a population of Ultra Compact Dwarf galaxies (UCDs) in the core region of the Coma Cluster. At the distance of Coma, UCDs are expected to have angular sizes 0.01 <R-e <0.2 arcsec. With ACS imaging, we can resolve all but the smallest ones with careful fitting. Candidate UCDs were chosen based on magnitude, color, and degree of resolution. We spectroscopically confirm 27 objects as bona fide UCD members of the Coma Cluster, a 60% success rate for objects targeted with M-R <-12. We attribute the high success rate in part to the high resolution of HST data and to an apparent large population of UCDs in Coma. We find that the UCDs tend to be strongly clustered around giant galaxies, at least in the core region of the cluster, and have a distribution and colors that are similar to globular clusters. These findings suggest that UCDs are not independent galaxies, but rather have a star cluster origin.