“One approach to the Strong CP Problem (known as Nelson-Barr models) is to assume that parity is a gauge symmetry which is spontaneously broken in the world around us. In this talk, I will argue that the domain walls formed from spontaneous parity breaking are exactly stable. This stability can be understood as the result of an unusual sort of conserved charge, which has features in common with both gauge charges and global charges. I will explain how these charges are compatible with the expected absence of global symmetries in quantum gravity.”