By considering a specific scenario of early language evolution, here I advocate taking into account one of the most obvious players in the evolution of human language capacity: (sexual) selection. The proposal is based both on an internal reconstruction using syntactic theory, and on comparative typological evidence, directly bringing together, formal, typological, and evolutionary considerations. As one possible test case, transitivity is decomposed into evolutionary primitives of syntactic structure, revealing a common denominator and the building blocks for crosslinguistic variation in transitivity. The approximations of this early grammar, identified by such a reconstruction, while not identical constructs, are at least as good proxies of the earliest stages of grammar as one can find among tools, cave paintings, or bird song. One subtype of such “living fossils” interacts directly with biological considerations of survival, aggression, and mate choice, while others clearly distinguish themselves in fMRI experiments. The fMRI findings are consistent with the proposal that the pressures to be able to master ever more and more complex syntax were at least partly responsible for driving the selection processes which gradually increased the connectivity of the Broca’s-basal ganglia network, crucial for syntactic processing, among other important functions.