Boron is an element of fascinating chemical complexity. Controversies have shrouded this element since its discovery was announced in 1808: the new 'element' turned out to be a compound containing less than 60-70% of boron, and it was not until 1909 that 99% pure boron was obtained. And although we now know of at least 16 polymorphs, the stable phase of boron is not yet experimentally established even at ambient conditions. Boron's complexities arise from frustration: situated between metals and insulators in the periodic table, boron has only three valence electrons, which would favour metallicity, but they are sufficiently localized that insulating states emerge. However, this subtle balance between metallic and insulating states is easily shifted by pressure, temperature and impurities. Here we report the results of high-pressure experiments and ab initio evolutionary crystal structure predictions that explore the structural stability of boron under pressure and, strikingly, reveal a partially ionic high-pressure boron phase. This new phase is stable between 19 and 89 GPa, can be quenched to ambient conditions, and has a hitherto unknown structure (space group Pnnm, 28 atoms in the unit cell) consisting of icosahedral B(12) clusters and B(2) pairs in a NaCl-type arrangement. We find that the ionicity of the phase affects its electronic bandgap, infrared adsorption and dielectric constants, and that it arises from the different electronic properties of the B(2) pairs and B(12) clusters and the resultant charge transfer between them.