For the first time an excess of photons above an energy threshold of 730 GeV from the giant radio galaxy M 87 has been measured at a significance level above 4 \sigma . The data have been taken during the years 1998 and 1999 with the HEGRA stereoscopic system of 5 imaging atmospheric Cherenkov telescopes . The excess of 107.4 \pm 26.8 events above 730 GeV corresponds to an integral flux of 3.3 % of the Crab flux or N _ { \gamma } ( E > 730 \mbox { GeV } ) = ( 0.96 \pm 0.23 ) \times 10 ^ { -12 } phot . cm ^ { -2 } s ^ { -1 } . M 87 is located at the center of the Virgo cluster of galaxies at a relatively small redshift of z = 0.00436 and is a promising candidate among the class of giant radio galaxies for the emission of TeV \gamma -radiation . The detection of TeV \gamma -rays from M 87 – if confirmed – would establish a new class of extragalactic source in this energy regime since all other AGN detected to date at TeV energies are BL Lac type objects .