ACTIVE galaxies are thought to be powered by the accretion of surrounding dust and gas onto central black holes. The unified model(1-3) of active galaxies predicts that narrow-line radio galaxies (NLRGs), which are very luminous at radio wavelengths and have narrow optical emission lines, would appear as quasars-which have broad emission lines-if viewed from a different direction. The nearby NLRG Cygnus A is the most luminous radio source in the local Universe, with a luminosity that lies within the range of that of quasars(4), but the polarization of optical light from this source seems at odds with the quasar model. Here we present evidence, in the form of broad ultraviolet line emission from singly ionized magnesium, that Cygnus A does indeed host a quasar.