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We study the thermal production of large-invariant-mass photon pairs emitted from a quark-gluon plasma at high temperature. To lowest order in perturbation theory the cross section for the annihilation process (qqBAR-->gamma-gamma) is known to lead to logarithmically divergent thermal production rates for massless quarks. We apply recently developed resummation methods of finite-temperature perturbation theory and show how screening effects on quarks in the plasma provide finite thermal rates for gamma-gamma pairs. We compare these results with previous estimates of gamma-gamma production rates. Finally, for the phenomenology of heavy-ion collisions we present the screened gamma-gamma emission spectra by taking into account the space-time history of these collisions.