We present a higher dimensional model where gravity is bound to a brane due to Anderson localization. The extra dimensions are taken to be a disordered crystal of branes, with randomly distributed tensions of order the fundamental scale. Such geometries bind the graviton and thus allow for arbitrarily large extra dimensions even when the curvature is small. Thus this model is quite distinct from that of Randall and Sundrum where localization is a consequence of curvature effects in the bulk. The hierarchy problem can be solved by having the standard model brane live a distance away from the brane on which the graviton is localized. The statistical properties of the system are worked out and it is shown that the scenario leads to a continuum of four dimensional theories with differing strengths of gravitational interactions. We live on one particular brane whose gravitational constant is G_N
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