H2O will be more resistant to metallization than previously thought. From computational evolutionary structure searches, we find a sequence of new stable and meta-stable structures for the ground state of ice in the 1–5 TPa (10 to 50 Mbar) regime, in the static approximation. The previously proposed Pbcm structure is superseded by a Pmc21 phase at p = 930 GPa, followed by a predicted transition to a P21 crystal structure at p = 1.3 TPa. This phase, featuring higher coordination at O and H, is stable over a wide pressure range, reaching 4.8 TPa. We analyze carefully the geometrical changes in the calculated structures, especially the buckling at the H in O-H-O motifs. All structures are insulating—chemistry burns a deep and (with pressure increase) lasting hole in the density of states near the highest occupied electronic levels of what might be component metallic lattices. Metallization of ice in our calculations occurs only near 4.8 TPa, where the metallic C2/m phase becomes most stable. In this regime, zero-point energies much larger than typical enthalpy differences suggest possible melting of the H sublattice, or even the entire crystal.