We construct planar black hole solutions in AdS < inf > 3 < /inf > and AdS < inf > 4 < /inf > in which the boundary CFT is perturbed by marginally relevant quenched disorder. We show that the entropy density of the horizon has the scaling temperature dependence s ∼ T < sup > (d−1)/z < /sup > (with d = 2, 3). The dynamical critical exponent z is computed numerically and, at weak disorder, analytically. These results lend support to the claim that the perturbed CFT flows to a disordered quantum critical theory in the IR.