The evolution of language required elaboration of a number of independent mechanisms in the hominin lineage, including systems involved in signaling, semantics, and syntax. Two perspectives on the evolution of syntax can be contrasted. The “continuist” perspective seeks the evolutionary roots of complex human syntax in simpler combinatory systems used in animal communication systems, such as iteration and sequencing. The “exaptationist” perspective posits evolutionary change of function, so that systems today used for linguistic communication might previously have served quite different functions in earlier hominids. I argue that abundant biological evidence supports an exaptationist perspective, in general, and that it must be taken seriously when considering language evolution. When applied to syntax, this suggests that core computational components used today in language could have originally served non-linguistic functions such as motor control, non-verbal thought, or spatial reasoning. I outline three specific exaptationist hypotheses for spoken language. These three hypotheses each posit a change of functionality in a precursor circuit, and its transformation into a neural circuit or region specifically involved in language today. Hypothesis 1 suggests that the precursor mechanism for intentional vocal control, specifically direct cortical control over the larynx, was manual motor control subserved by the cortico-spinal tract. The second is that the arcuate fasciculus, which today connects syntactic and lexical regions, had its origin in intracortical connections subserving vocal imitation. The third is that the specialized components of Broca’s area, specifically BA 45, had their origins in non-linguistic motor control, and specifically hierarchical planning of action. I conclude by illustrating the importance of both homology (studied via primates) and convergence (typically analyzed in birds) for testing such evolutionary hypotheses.