We search for the radiative leptonic tau decays τ→ee+e−ντνe and τ→μe+e−ντνμ using 3.60fb−1 of data collected by the CLEO-II experiment at the Cornell Electron Storage Ring. We present a first observation of the τ→ee+e−ντνe process. For this channel we measure the branching fraction B(τ→ee+e−ντνe) = (2.7+1.5+0.4+0.1−1.1−0.4−0.3)×10−5. An upper limit is established for the second channel: B(τ→μe+e−ντνμ) < 3.2 × 10−5 at 90% C.L. Both results are consistent with the rates expected from standard model predictions.