Estimate of B(B(over) -->Xgamma) at O(alpha(s)2).

Combining our results for various O(alpha[s]) corrections to the weak radiative B-meson decay, we are able to present the first estimate of the branching ratio at the next-to-next-to-leading order in QCD. We find B(B[over ]-->X[s]gamma)=(3.15+/-0.23) x 10(-4) for Egamma>1.6 GeV in the B[over ]-meson rest frame. The four types of uncertainties:nonperturbative (5%), parametric (3%), higher-order (3%), and m(c)-interpolation ambiguity (3%) have been added in quadrature to obtain the total error.