New evidence is presented that EUV emission lines formed at the levels of the base of the corona and the transition region are systematically shifted to shorter wavelengths within coronal holes relative to the rest of the solar disk, and that moreover this shift increases with height in the atmosphere. Measurements were made with a rocket-borne EUV spectrometer having high spectroscopic resolution and stability flown on July 15, 1980. Repeated measurements were made along a chord of the solar disk that crossed a compact coronal hole near sun center identified on gamma 10830 He I spectroheliograms. The maximum measured shift corresponded to a velocity of 12 km/sec in gamma 625 Mg X and 7 km/sec in gamma 629 O V. If these velocities correspond to a true mass flux, they provide important data on the acceleration of coronal plasma in open magnetic field regions. These observed Doppler displacements are a strong and significant signature of coronal holes, now measured on three rocket flights.