Compton scattering on the deuteron is studied in the framework of baryon ch
iral perturbation theory to third order in small momenta, for photon energi
es of order the pion mass. The scattering amplitude is a sum of one- and tw
o-nucleon mechanisms with no undetermined parameters. Our results are in go
od agreement with existing experimental data, and a prediction is made for
higher-energy data being analyzed at SAL, (C) 1999 Elsevier Science B.V. Al
l rights reserved.