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The emission of hard real photons from a quark-gluon plasma at high temperatures is studied. At lowest order the QCD processes for quark-antiquark annihilation (qqBAR --> gamma-g) and for Compton scattering (qg --> gamma-q) lead to logarithmically divergent thermal production rates for massless quarks. By applying recently developed resummation methods of finite temperature perturbation theory we show that effects due to Landau damping on the exchanged quark provide finite rates. Comparisons with previous estimates and phenomenological implications are discussed.