A search for lepton flavor violating decays of a tau to a lighter-mass charged lepton and an omega vector meson is performed using 384.1 fb(-1) of e(+)e(-) annihilation data collected with the BABAR detector at the Stanford Linear Accelerator Center PEP-II storage ring. No signal is found, and the upper limits on the branching ratios are determined to be B(tau(+/-)-->e;{+/-}omega)<1.1 x10 (-7) and B(tau(+/-)-->micro(+/-)omega)<1.0 x 10(-7) at 90% confidence level.