Magnetic fields change the way that electrons move through solids. The nature of these changes reveals information about the electronic structure of a material and, in auspicious circumstances, can be harnessed for applications. The silver chalcogenides, Ag2Se and Ag2Te, are non-magnetic materials, but their electrical resistance can be made very sensitive to magnetic field by adding small amounts--just 1 part in 10,000--of excess silver. Here we show that the resistance of Ag2Se displays a large, nearly linear increase with applied magnetic field without saturation to the highest fields available, 600,000 gauss, more than a million times the Earth's magnetic field. These characteristics of large (thousands of per cent) and near-linear response over a large field range make the silver chalcogenides attractive as magnetic-field sensors, especially in physically tiny megagauss (10(6) G) pulsed magnets where large fields have been produced but accurate calibration has proved elusive. High-field studies at low temperatures reveal both oscillations in the magnetoresistance and a universal scaling form that point to a quantum origin for this material's unprecedented behaviour.