  The Einstein Equivalence Principle (EEP) can be probed with astrophysical
sources emitting simultaneously different types of neutral particles, or
particles with varying energies, by testing their time of flight through the
same gravitational field. Here we use the time delays between correlated
photons from cosmological transients to constrain the accuracy of the EEP. We
take data from two gamma-ray bursts as an example, and use, as a lower limit to
the theoretical time delays between different energies, delays arising from
only the gravitational field of our own galaxy. We then show that the
parameterized post-Newtonian parameter $\gamma$ is the same for photons over
energy ranges between eV and MeV and between MeV and GeV to a part in
$10^{-7}$, which is at least one order of magnitude better than previous
limits. Combining this bound on the wavelength dependence of $\gamma$ with the
absolute bound $|\gamma-1|<0.3\%$ from light-deflection measurements at optical
(eV) wavelengths, we thus extend this absolute bound on $\gamma$ to GeV
energies.
