  We formulate a new power-counting scheme for a chiral effective field theory
of nucleons, pions, and Deltas. This extends chiral perturbation theory into
the Delta-resonance region. We calculate nucleon Compton scattering up to
next-to-leading order in this theory. The resultant description of existing
$\gamma$p cross section data is very good for photon energies up to about 300
MeV. We also find reasonable numbers for the spin-independent polarizabilities
$\alpha_p$ and $\beta_p$.
