  We present calculations of differential cross sections for Compton scattering
from the proton, using amplitudes calculated to fourth order in heavy baryon
chiral perturbation theory. We compare with available data up to 200 MeV. We
find that the agreement for angles below 90 degree is acceptable over the whole
energy range, but that at more backward angles the agreement decreases above
about 100 MeV, and fails completely above the photoproduction threshold.
