  We present the next-to-next-to-leading order ($alpha alpha_s^2$) corrections
to the first moment of the polarized virtual photon structure function
$g_1^gamma(x,Q^2,P^2)$ in the kinematical region $Lambda^2 ll P^2 ll Q^2$,
where $-Q^2(-P^2)$ is the mass squared of the probe (target) photon and
$Lambda$ is the QCD scale parameter. In order to evaluate the three-loop-level
photon matrix element of the flavor singlet axial current, we resort to the
Adler-Bardeen theorem for the axial anomaly and we calculate in effect the
two-loop diagrams for the photon matrix element of the gluon operator. The
$alpha alpha_s^2$ corrections are found to be about 3% of the sum of the
leading order ($alpha$) andthe next-to-leading order ($alpha alpha_s$)
contributions, when $Q^2=30 sim 100 {rm GeV}^2$and $P^2=3{rm GeV}^2$, and the
number of active quark flavors $n_f$ is three to five.
