Observeration of Radiative Leptonic Decay of the Tau Lepton

Using 4.68 fb^{-1} of e^+e^- annihilation data collected with the CLEO II detector 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 a tau radiatively decaying to a muon is measured to be (3.61+-0.16+-0.35)*10^{-3}, and to an electron is (1.75+-0.06+-0.17)*10^{-2}. The branching fractions are in agreement with the Standard Model theoretical predictions. All quoted results are preliminary.