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