  We compute the charged pion loop contribution to the light-by-light
scattering amplitude for off-shell photons in chiral perturbation theory
through next-to-leading order (NLO). We show that NLO contributions are
relatively more important due to a fortuitous numerical suppression of the
leading-order (LO) terms. Consequently, one expects theoretical predictions for
the hadronic light-by-light (HLBL) contribution to the muon anomalous magnetic
moment, $a_\mu^{HLBL}$, to be sensitive to the choice of model for the higher
momentum-dependence of the LBL amplitude. We show that models employed thus far
for the charged pion loop contribution to $a_\mu^{HLBL}$ are not consistent
with low-momentum behavior implied by quantum chromodynamics, having omitted
potentially significant contributions from the pion polarizability.
