  We present the two-loop matrix elements for the scattering of two gluons into
two photons in QCD. These matrix elements will enter into improved estimates of
the QCD background to Higgs production at the LHC when the Higgs decays into
two photons. The photon mode is especially important if M_H < 140 GeV. We also
give the amplitudes for the crossed process, glue gamma to glue gamma.
