  The calculation of the $O(\a_s)$ virtual corrections to the matrix element of
the inclusive decay $b \to s \gamma$ is reported. These contributions
drastically reduce the large renormalization scale dependence of the leading
logarithmic calculation. Combining these results with the preliminary result
for the Wilson coefficient $C_7(m_b)$ calculated recently by Chetyrkin, Misiak,
and M\"unz, we estimate the branching ratio to be $BR(B \to X_s \gamma)=(3.25
\pm 0.50) \times 10^{-4}$.
