The origin of longstanding anomalies in experimental studies of the dense solid phases of H2O ices VII, VIII, and X is examined using a combination of first-principles theoretical methods. We find that a ferroelectric variant of ice VIII is energetically competitive with the established antiferroelectric form under pressure. The existence of domains of the ferroelectric form within anti-ferroelectric ice can explain previously observed splittings in x-ray diffraction data. The ferroelectric form is stabilized by density and is accompanied by the onset of spontaneous polarization. The presence of local electric fields triggers the preferential parallel orientation of the water molecules in the structure, which could be stabilized in bulk using new high-pressure techniques.