Search for Lepton Flavor Violation in the Decay<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>τ</mml:mi><mml:mo>±</mml:mo></mml:msup><mml:mo>→</mml:mo><mml:msup><mml:mi>μ</mml:mi><mml:mo>±</mml:mo></mml:msup><mml:mi>γ</mml:mi></mml:math>

A search for the nonconservation of lepton flavor number in the decay tau(+/-) --> mu(+/-) has been performed using 2.07 x 10(8) e(+ )e(-) tau(+) tau(-) events produced at a center-of-mass energy near 10.58 GeV with the BABAR detector at the PEP-II storage ring. We find no evidence for a signal and set an upper limit on the branching ratio of Beta(tau(+/-) --> mu(+/-) gamma) < 6.8 x 10(-8) at 90% confidence level.