The tau lepton electron branching fraction has been measured with the CLEO II detector at the Cornell Electron Storage Ring as [ital B][sub [ital e]]=0.1749[plus minus]0.0014[plus minus]0.0022, with the first error statistical and the second systematic. The measurement involves counting electron-positron annihilation events in which both taus decay to electrons, and normalizing to the number of tau-pair decays expected from the measured luminosity. Detected photons in these events constitute a definitive observation of tau decay radiation.