We demonstrate quantum walks of a photon pair in a spatially extended Einstein-Podolsky-Rosen state coupled into an on-chip multiport photonic lattice. By varying the degree of entanglement we observe Anderson localization for pairs in a separable state and Anderson colocalization for pairs in an Einstein-Podolsky-Rosen entangled state. In the former case, each photon localizes independently, while in the latter neither photon localizes, but the pair colocalizes--revealing unexpected survival of the spatial correlations through strong disorder.