Abstract: | A search for the decays B-->rho(770)gamma and B0-->omega(782)gamma is performed on a sample of 211 x 10(6) Upsilon(4S)-->BB events collected by the BABAR detector at the SLAC PEP-II asymmetric-energy e(+)e(-) storage ring. No evidence for the decays is seen. We set the following limits on the individual branching fractions: B(B+-->rho(+)gamma)<1.8 x 10(-6), B(B0-->rho(0)gamma)<0.4 x 10(-6), and B(B0-->omegagamma)<1.0 x 10(-6) at the 90% confidence level. We use the quark model to limit the combined branching fraction B [B-->(rho/omega)gamma]<1.2 x 10(-6), from which we determine a constraint on the ratio of Cabibbo-Kobayashi-Maskawa matrix elements |V(td)|/|V(ts)|. |