Piezoelectric materials have many applications at cryogenic temperatures. However, the piezoelectric response below 10 kelvin is diminished, making the use of these materials somewhat marginal. Results are presented on strontium titanate (SrTiO3), which exhibits a rapidly increasing piezoelectric response with decreasing temperature below 50 kelvin; the magnitude of its response around 1 kelvin is comparable to that of the best materials at room temperature. This 'giant' piezoelectric response may open the way for a broad class of applications including use in ultralow-temperature scanning microscopies and in a magnetic field- insensitive thermometer. These observations, and the possible divergence of the mechanical response to electric fields at even lower temperatures, may arise from an apparent quantum critical point at absolute zero.