  For the gamma-pion interaction, the perturbative expansion of the effective
chiral Lagrangian (chi-PT) can be limited to terms quartic in momenta and
masses (O(p4)), or to higher order. The abnormal intrinsic parity (chiral
anomaly) component of the lagrangian leads to interesting predictions for the
processes pi0 -----> 2 gamma and gamma ----->3 pi. These are described by the
amplitudes F_{pi} and F_{3pi}, respectively. We demonstrate that the O(p4)
value of F_{3pi} disagrees with existing data, while the O(p6) value is nearly
consistent. We describe how Fermilab experiment E781 can get improved data for
tests of the chiral anomaly.
