Metals cannot exhibit ferroelectricity because static internal electric fields are screened by conduction electrons, but in 1965, Anderson and Blount predicted the possibility of a ferroelectric metal, in which a ferroelectric-like structural transition occurs in the metallic state. Up to now, no clear example of such a material has been identified. Here we report on a centrosymmetric (R3c) to non-centrosymmetric (R3c) transition in metallic LiOsO3 that is structurally equivalent to the ferroelectric transition of LiNbO3 (ref. 3). The transition involves a continuous shift in the mean position of Li(+) ions on cooling below 140 K. Its discovery realizes the scenario described in ref. 2, and establishes a new class of materials whose properties may differ from those of normal metals.