  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.
