We e v aluate the amplitude for ! 0 0 to two loops in chiral perturbation theory. The three new counterterms which e n ter at this order in the lowenergy expansion are estimated with resonance saturation. We nd that the cross section agrees rather well with the available data and with dispersion theoretic calculations even substantially above threshold. Numerical results for the Compton cross section and for the neutral pion polarizabilities are also given to two-loop accuracy.]