Critical scaling at zero virtuality in QCD

We show that at the critical point of chiral random matrix models, novel scaling laws for the inverse moments of the eigenvalues are expected. We evaluate explicitly the pertinent microscopic spectral density, and find it in agreement with numerical calculations. We suggest that similar sum rules are of relevance to QCD at the critical temperature, and even above if the transition is amenable to a Ginzburg-Landau description.