Using data from the Imaging Proportional Counter on the Einstein Observatory, we search for X-ray emission from 45 early-type galaxies in Coma. Some galaxies lying within 13' of the cluster center give statistically significant signals which, however, we determine to be spurious. Data for a clean subsample of 27 observations of galaxies greater than 13' from the cluster center yield only upper limits, which are generally larger than those of field ellipticals with similar optical luminosities. The mean galaxy X-ray and blue luminosities for the subsample are <L(X)> < 2.2 x 10(40) ergs s-1 and <L(B)> = 4.4 x 10(10) L., respectively. This X-ray limit lies well within the range observed for field galaxies and near the value estimated for a galaxy devoid of a hot interstellar medium. We can exclude the hypothesis that Coma Cluster galaxies show excess emission, such as has been attributed to galaxies in A1367, and we conclude that environmental effects in rich clusters do not enhance the X-ray emission from individual elliptical galaxies. Conclusive evidence that the emission is strongly suppressed, e.g., by stripping of the interstellar gas, must await more sensitive studies.