Magnetoresistance is the change in a material's electrical resistance in response to an applied magnetic field. Materials with large magnetoresistance have found use as magnetic sensors, in magnetic memory, and in hard drives at room temperature, and their rarity has motivated many fundamental studies in materials physics at low temperatures. Here we report the observation of an extremely large positive magnetoresistance at low temperatures in the non-magnetic layered transition-metal dichalcogenide WTe2: 452,700 per cent at 4.5 kelvins in a magnetic field of 14.7 teslas, and 13 million per cent at 0.53 kelvins in a magnetic field of 60 teslas. In contrast with other materials, there is no saturation of the magnetoresistance value even at very high applied fields. Determination of the origin and consequences of this effect, and the fabrication of thin films, nanostructures and devices based on the extremely large positive magnetoresistance of WTe2, will represent a significant new direction in the study of magnetoresistivity.