PHOTONS of TeV energy have been observed from a few sources in our Galaxy, notably the Crab Nebula1. We report here the detection of such photons from an extragalactic source, the giant elliptical galaxy Markarian 421. Mk 421 has a nucleus of the BL Lacertae type2,3, and emission from it has been observed at radio4–6, optical3,6 and X-ray6–8 frequencies, and most recently in the MeV-GeV bands, by the EGRET detector aboard the Compton observatory9. In March–June 1992, we observed Mk 421 with the Whipple Observatory γ-ray telescope10, a ground-based detector that images Cerenkov light from air showers, and found a signal with statistical significance of 6er above background. The flux above 0.5 TeV is 0.3 of that from the Crab Nebula. The source location agrees with the position of Mk 421 within the angular uncertainty (6 arc minutes) of the Whipple instrument. The fact that we have observed this relatively nearby source (redshift z = 0.031), whereas active galaxies and quasars that are brighter at EGRET energies but more distant have not been detected in the TeV energy range, may be consistent with suggestions11,12 that TeV photons are strongly attenuated by interaction with extragalactic starlight.