Our core hypothesis is that the emergence of our species-specific language-ready brain ought to be understood in light of the developmental changes expressed at the levels of brain morphology and neural connectivity that occurred in our species after the split from Neanderthals-Denisovans and that gave us a more globular braincase configuration. In addition to changes at the cortical level, we hypothesize that the anatomical shift that led to globularity also entailed significant changes at the subcortical level. We claim that the functional consequences of such changes must also be taken into account to gain a fuller understanding of our linguistic capacity. Here we focus on the thalamus, which we argue is central to language and human cognition, as it modulates fronto-parietal activity. With this new neurobiological perspective in place, we examine its possible molecular basis. We construct a candidate gene set whose members are involved in the development and connectivity of the thalamus, in the evolution of the human head, and are known to give rise to language-associated cognitive disorders. We submit that the new gene candidate set opens up new windows into our understanding of the genetic basis of our linguistic capacity. Thus, our hypothesis aims at generating new testing grounds concerning core aspects of language ontogeny and phylogeny.