Observation of Radiative Leptonic Decay of the Tau Lepton

Using 4.68 fb^{-1} of e^+e^- annihilation data collected with the CLEO II detector at the Cornell Electron Storage Ring (CESR) we have studied tau radiative decays tau -> mu nu nu gamma and tau -> e nu nu gamma. For a 10 MeV minimum photon energy in the tau rest frame, the branching fraction of radiative tau decay to a muon or electron is measured to be (3.61+-0.16+-0.35)*10^{-3} or (1.75+-0.06+-0.17)*10^{-2}, respectively. The branching fractions are in agreement with the Standard Model theoretical predictions.