  The neutral pion photoproduction on the proton near threshold has a very
small scattering cross section when compared to the charged channels, which in
ChPT is explained by strong cancellations between the lowest order pieces.
Therefore it is very sensitive to higher-order corrections of chiral
perturbation theory. We perform a fully covariant calculation up to chiral
order p^3 and we investigate the effect of the inclusion of the Delta(1232)
resonance as an explicit degree of freedom. We show that the convergence
improves, leading to a much better agreement with data at a wide range of
energies.
