Abstract: Under pressure, metals exhibit increasingly shorter interatomic distances. Intuitively, this response is expected to be accompanied by an increase in the widths of the valence and conduction bands and hence a more pronounced free-electron-like behaviour. But at the densities that can now be achieved experimentally, compression can be so substantial that core electrons overlap. This effect dramatically alters electronic properties from those typically associated with simple free-electron metals, leading in turn to structurally complex phases and electronic properties. But the most intriguing prediction——that the seemingly simple metals Li and Na will transform under pressure into insulating states, owing to pairing of alkali atoms——has yet to be experimentally confirmed. Here, combining theory with experiment, we find that the metal Na transforms into an optically transparent insulating phase at 200GPa with a wide band gap. The insulating phase of Na possesses a six-coordinated, highly distorted double-hexagonal close-packed structure. We attribute the emergence of this dense insulating state not to atom pairing, but to p-d hybridizations of valence electrons and their repulsion by core electrons into the lattice interstices. We expect that such insulating states may also form in other elements and compounds when compression is sufficiently strong that atomic cores start to overlap strongly.