With the discovery(1) of superconductivity at 203 kelvin in H3S, attention returned to conventional superconductors with properties that can be described by the Bardeen-Cooper-Schrieffer and the Migdal-Eliashberg theories. Although these theories predict the possibility of room-temperature superconductivity in metals that have certain favourable properties-such as lattice vibrations at high frequencies-they are not sufficient to guide the design or predict the properties of new superconducting materials. First-principles calculations based on density functional theory have enabled such predictions, and have suggested a new family of superconducting hydrides that possess a clathrate-like structure in which the host atom (calcium, yttrium, lanthanum) is at the centre of a cage formed by hydrogen atoms(2-4). For LaH10 and YH10, the onset of superconductivity is predicted to occur at critical temperatures between 240 and 320 kelvin at megabar pressures(3-6). Here we report superconductivity with a critical temperature of around 250 kelvin within the Fm (3) over barm structure of LaH10 at a pressure of about 170 gigapascals. This is, to our knowledge, the highest critical temperature that has been confirmed so far in a superconducting material. Superconductivity was evidenced by the observation of zero resistance, an isotope effect, and a decrease in critical temperature under an external magnetic field, which suggested an upper critical magnetic field of about 136 tesla at zero temperature. The increase of around 50 kelvin compared with the previous highest critical temperature(1) is an encouraging step towards the goal of achieving room-temperature superconductivity in the near future.