Femtosecond electron bunches with keV energies and eV energy spread are needed by condensed matter physicists to resolve state transitions in carbon nanotubes, molecular structures, organic salts, and charge density wave materials. These semirelativistic electron sources are not only of interest for ultrafast electron diffraction, but also for electron energy-loss spectroscopy and as a seed for x-ray FELs. Thus far, the output energy spread (hence pulse duration) of ultrafast electron guns has been limited by the achievable electric field at the surface of the emitter, which is 10 MV/m for DC guns and 200 MV/m for RF guns. A single-cycle THz electron gun provides a unique opportunity to not only achieve GV/m surface electric fields but also with relatively low THz pulse energies, since a single-cycle transform-limited waveform is the most efficient way to achieve intense electric fields. Here, electron bunches of 50 fC from a flat copper photocathode are accelerated from rest to tens of eV by a microjoule THz pulse with peak electric field of 72 MV/m at 1 kHz repetition rate. We show that scaling to the readily-available GV/m THz field regime would translate to monoenergetic electron beams of ~100 keV.