  In view of ongoing experimental activities to determine the pion
polarizabilities, we have started to recalculate the available two-loop
expressions in the framework of chiral perturbation theory, because they have
never been checked before. We make use of the chiral Lagrangian at order p^6
now available, and of improved techniques to evaluate the two-loop diagrams.
Here, we present the result for the neutral pions. The cross section for the
reaction gamma+gamma->pi0+pi0 agrees with the earlier calculation within a
fraction of a percent. We present analytic results for the dipole and
quadrupole polarizabilities, and compare the latter with a recent evaluation
from data on gamma+gamma->pi0+pi0.
