The ~70 unidentified sources of the EGRET sky survey may be one of its most important legacies. The identification of these sources at other wavelengths is critical to understanding their nature. Many have flat spectra out to 10 GeV which, if extrapolated to TeV energies, would be easily detectable relative to the steeply falling diffuse background. The Whipple Observatory gamma-ray telescope has been used to observe a number of these which were selected based on their position, intensity and spectrum and in some cases based on a possible association with a supernova remnant or pulsar. No significant emission has been detected from these sources, and upper limits are given.