  A search for the exclusive radiative decays B --> rho(770) gamma and B0 -->
omega(782) gamma is performed on a sample of about 84\times 10^{6} B\bar B
events collected by the BaBar detector at the PEP-II asymmetric-energy e+e-
storage ring. No significant signal is seen in any of the channels. We set
upper limits on the branching fractions of BR(B^0 -> rho^0 gamma) < 1.2 \times
10^{-6}, BR(B^+ -> rho^+ gamma) < 2.1 \times 10^{-6}, and BR(B^0 -> omega
gamma) < 1.0 \times 10^{-6} at 90% confidence level (C.L.). Using the
assumption that Gamma(B --> rho gamma) = Gamma(B+ --> rho+ gamma)
=2\times\Gamma(B0 --> rho0 gamma), we find the combined limit BR(B --> rho
gamma)<1.9 \times 10^{-6}, corresponding to BR(B --> rho gamma)/\BR(B --> K*
gamma) < 0.047 at 90% C.L.
