It is demonstrated that interfacial dislocations may be formed spontaneously when a thin film of rubbery polymer is peeled from a smooth glass surface at a low angle. The effect of these dislocations is to stop the peeling, thereby significantly increasing the strength of the adhesive joint. Theoretical analysis shows that such dislocations result from a combination of peeling where the surfaces separate and healing where the surfaces naturally come together and reconstitute the joint as a consequence of the surface attractions between the peeled bodies. It is this spontaneous healing, shown experimentally to exhibit a curious time decay, which determines the formation and geometry of the peel dislocations.