We report an analysis of tau;{-} decaying into omegapi;{-}nu_{tau} with omega --> pi;{+}pi;{-}pi;{0} using a data sample containing nearly 320 x 10;{6}tau pairs collected with the BABAR detector at the PEP-II B-Factory. We find no evidence for second-class currents, and we set an upper limit of 0.69% at 90% confidence level for the fraction of second-class currents in this decay mode.