Grammaticalization as standardly conceived is a change whereby an item develops from a lexical to a grammatical or functional meaning, or from being less to more grammatical. In this article we show that this can only be part of the story; for a full account we need to understand the syntactic structures into which grammaticalizing elements fit and how they too develop. To achieve this end we consider in detail the history of definiteness marking within the noun phrase in North Germanic, and in particular in Faroese. We show how this change requires us to distinguish between projecting and nonprojecting categories, and how a category can emerge over time and only subsequently develop into a head with its own associated functional projection. The necessary structure, rather than being intrinsic to an aprioristic universal grammar, grows over time as part of the grammaticalization process. We suggest that this in turn argues for a parallel correspondence theory of grammar such as the one adopted here, LEXICAL-FUNCTIONAL GRAMMAR, in which different dimensions of linguistic structure can change at different rates.