Using 4.68 fb(-1) of e(+) e(-) annihilation data collected with the CLEO II
detector at the Cornell Electron Storage Ring, we have studied tau radiati
ve decays tau(-) --> nu(tau)mu(-)<<(nu)over bar>(mu)gamma and tau- --> nu(t
au)e(-)<(nu)over bar>(e)gamma. For a 10 MeV minimum photon energy in the ta
u rest frame, the branching fraction for radiative tau decay to a muon or e
lectron is measured to be (3.61 +/- 0.16 +/- 0.35) x 10(-3) or (1.75 +/- 0.
06 +/- 0.17) x 10(-2), respectively. The branching fractions are in agreeme
nt with standard model theoretical predictions.