A material as hard as diamond or cubic boron nitride has yet to be identified, but here we report the discovery of a cotunnite-structured titanium oxide which represents the hardest oxide known. This is a new polymorph of titanium dioxide, where titanium is nine-coordinated to oxygen in the cotunnite (PbCl2) structure. The phase is synthesized at pressures above 60 gigapascals (GPa) and temperatures above 1,000 K and is one of the least compressible and hardest polycrystalline materials to be described.