Polarized double photon production in QCD to order alpha s.

We present a complete order $\alpha_s$ analysis of the process $p p\to \gamma \gamma + X$ with polarized initial states, previously studied by us with leading order structure functions. We include in our calculation new sets of parton densities evolved in NLO QCD, such as those of Gehrmann and Stirling and of Gl\"{u}ck et al., which incorporate the new anomalous dimensions of Mertig and Van Neerven in the evolution equation. A detailed phenomenological analysis is also given which includes the photon isolation. Our results indicate that the asymmetries, although not very large, should be substantial enough at RHIC energies to be measurable in future planned experiments.