  We calculate the $O(\a_s)$ virtual corrections to the matrix element for $b
\to s \gamma$, taking into account the contributions of the four-Fermi operator
$O_2$ and the electromagnetic and color dipole-type operators. The results are
combined with existing $O(\a_s)$ Bremsstrahlung corrections in order to obtain
the relevant inclusive rate. The new result drastically reduces the large scale
dependence of the leading logarithmic approximation. It implies that a very
accurate prediction for the branching ratio for $B \to X_s \g $ will become
possible once also the corrections to the Wilson coefficients are available.
