We've discussed this before several times (here, here, and here, for example). The direct experiment (making some anti-hydrogen so that you've got electrically neutral anti-matter, but still keeping it contained and then watching to see how quickly it falls) hasn't been done yet, although I think at this point the AEGIS group at CERN are only a couple years away from being able to do it. However, there are some pretty sound theoretical arguments, based on some fairly straightforward observations and measurements, that antimatter should respond the same as normal matter in a gravitational field.
Conserve energy. Commute with the Hamiltonian.