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The anomalous nondipolar and nonaxisymmetric magnetic fields of Uranus and Neptune have long challenged conventional views of planetary dynamos. A thin-shell dynamo conjecture captures the observed phenomena but leaves unexplained the fundamental material basis and underlying mechanism. Here we report extensive quantum-mechanical calculations of polymorphism in the hydrogen–oxygen system at the pressures and temperatures of the deep interiors of these ice giant planets (to >600 GPa and 7,000 K). The results reveal the surprising stability of solid and fluid trihydrogen oxide (H 3 O) at these extreme conditions. Fluid H 3 O is metallic and calculated to be stable near the cores of Uranus and Neptune. As a convecting fluid, the material could give rise to the magnetic field consistent with the thin-shell dynamo model proposed for these planets. H 3 O could also be a major component in both solid and superionic forms in other (e.g., nonconvecting) layers. The results thus provide a materials basis for understanding the enigmatic magnetic-field anomalies and other aspects of the interiors of Uranus and Neptune. These findings have direct implications for the internal structure, composition, and dynamos of related exoplanets.