  In this analysis, we present the contribution associated with the
chromomagnetic dipole operator O_8 to the double differential decay width
d\Gamma/(ds_1 ds_2) for the inclusive process $\bar{B} \to X_s \gamma \gamma$.
The kinematical variables s_1 and s_2 are defined as s_i=(p_b - q_i)^2/m_b^2,
where p_b, q_1, q_2 are the momenta of b-quark and two photons. This
contribution (taken at tree level) is of order \alpha_s, like the recently
calculated QCD corrections to the contribution of the operator O_7. In order to
regulate possible collinear singularities of one of the photons with the
strange quark, we introduce a non zero mass m_s for the strange quark. Our
results are obtained for exact m_s, which we interpret as a constituent mass
being varied between 400 and 600 MeV. Numerically it turns out that the effect
of the (O_8, O_8) contribution to the branching ratio of $\bar{B} \to X_s
\gamma \gamma$ does not exceed +0.1 % for any kinematically allowed value of
our physical cutoff parameter c, confirming the expected suppression of this
contribution relative to the QCD corrections to d\Gamma_{77}/(ds_1 ds_2).
