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We calculate the production rate of soft real photons from a hot quark-gluon plasma using Braaten-Pisarski's perturbative resummation method. To leading order in the QCD coupling constant g we find a logarithmically divergent result for photon energies of order gT, where T is the plasma temperature. This divergent behaviour is due to unscreened mass singularities in the effective hard thermal loop vertices in the case of a massless external photon.