  The measurement of an excess in the cosmic-ray electron spectrum between 300
and 800 GeV by the ATIC experiment has - together with the PAMELA detection of
a rise in the positron fraction up to 100 GeV - motivated many interpretations
in terms of dark matter scenarios; alternative explanations assume a nearby
electron source like a pulsar or supernova remnant. Here we present a
measurement of the cosmic-ray electron spectrum with H.E.S.S. starting at 340
GeV. While the overall electron flux measured by H.E.S.S. is consistent with
the ATIC data within statistical and systematic errors, the H.E.S.S. data
exclude a pronounced peak in the electron spectrum as suggested for
interpretation by ATIC. The H.E.S.S. data follow a power-law spectrum with
spectral index of 3.0 +- 0.1 (stat.) +- 0.3 (syst.), which steepens at about 1
TeV.
