A search for the nonconservation of lepton flavor in the decay tau+/--->e+/-gamma has been performed with 2.07x10(8) e+e--->tau+tau- events collected by the BABAR detector at the SLAC PEP II storage ring at a center-of-mass energy near 10.58 GeV. We find no evidence for a signal and set an upper limit on the branching ratio of Beta(tau+/--->e+/-gamma)<1.1x10(-7) at 90% confidence level.