The very large collection area of ground-based gamma-ray telescopes gives them a substantial advantage over balloon or satellite based instruments in the detection of very-high-energy (>600 GeV) cosmic-ray electrons. Here we present the electron spectrum derived from data taken with the High Energy Stereoscopic System (H.E.S.S.) of imaging atmospheric Cherenkov telescopes. In this measurement, the first of this type, we are able to extend the measurement of the electron spectrum beyond the range accessible to direct measurements. We find evidence for a substantial steepening in the energy spectrum above 600 GeV compared to lower energies.