We report results of a search for the rare radiative decay (B) over bar(0)
--> D*(0)gamma. Using 9.66 x 10(6) <B(B)over bar> meson pairs collected wit
h the CLEO detector at the Cornell Electron Storage Ring, we set an upper l
imit on the branching ratio for this decay of 5.0 x 10(-5) at 90% C.L. This
provides evidence that the anomalous enhancement is absent in W-exchange p
rocesses and that weak radiative B decays are dominated by the short-distan
ce b --> s gamma mechanism in the standard model.