The microscopic structure of ice poses a long-standing challenge to theory(1-3). Because of their low mass, the protons in the hydrogen bonds that define the structures of crystalline ice are susceptible to quantum-mechanical effects such as tunnelling(1,4-8). High pressure pro,ides a means of controlling the length of the hydrogen bonds in order to investigate such effects, In particular, Holzapfel predicted 26 years ago that, under pressure, hydrogen bonds might be transformed from the highly asymmetric O-H ... O configuration to a symmetric state in which the proton lies midway between the two oxygens(9), leading to a non-molecular symmetric phase of ice, now denoted as ice ＇X＇. The existence of this phase has been inferred from spectroscopy(10-14), but has still not been observed directly, Here we investigate the role of quantum effects in proton ordering and hydrogen-bond symmetrization within ice at high pressure by using a simulation technique that treats both electrons and nuclei quantum-mechanically(15-17). We find that the proton-ordered structure at low pressure, with asymmetric hydrogen bonds (ice VIII), transforms on increasing pressure to a proton-disordered asymmetric I phase (ice VII) owing to translational proton tunnelling, On further compression, the zero-point fluctuations lead to strongly delocalized protons and hydrogen-bond symmetrization, even though the underlying character of the proton-transfer potential remains a double well, Only at still higher pressures does the double-well potential become transformed into a single well, whereupon the protons again become increasingly localized.