In Jackendoff's Parallel Architecture, the well-formed expressions of a language are licensed by correspondences between phonology, syntax, and conceptual structure. I show how this architecture can be used to make sense of the existence of parasitic gap constructions. A parasitic gap is one that is rendered acceptable because of the presence of another gap in the same sentence. Compare *"a person who[subscript i] everyone who talks to t[subscript i] likes Chris," which shows an illicit extraction from a relative clause, and "a person who[subscript i] everyone who talks to pg[subscript i] likes t[subscript i]," which shows a parasitic gap in the relative clause. Languages differ in terms of the range of configurations in which they allow parasitic gaps; these configurations appear to form a hierarchy. These observations raise some fundamental questions: Why do parasitic gaps exist at all? Why are different syntactic configurations possible for P-gaps and why just these configurations? Why is there a parasitic gap hierarchy? The answers that I propose make crucial use of constructional overgeneralization of across-the-board extraction in coordinate constructions, formulated straightforwardly in the framework of Jackendoff's Parallel Architecture.