The Laguna del Maule (LdM) volcanic field in Chile is an exceptional example of postglacial rhyolitic volcanism in the Southern Volcanic Zone of the Andes. By interferometric analysis of synthetic aperture radar (SAR) images acquired between 2007 and 2012, we measure exceptionally rapid deformation. The maximum vertical velocity exceeds 280 mm yr(-1). Although the rate of deformation was negligible from 2003 January to 2004 February, it accelerated some time before 2007 January. Statistical testing rejects, with 95 per cent confidence, four hypotheses of artefacts caused by tropospheric gradients, ionospheric effects, orbital errors or topographic relief, respectively. The high rate of deformation is confirmed by daily estimates of position during several months in 2012, as measured by analysis of signals transmitted by the Global Positioning System (GPS) and received on the ground at three stations around the reservoir forming the LdM. The fastest-moving GPS station (MAU2) has a velocity vector of [-180 +/- 4, 46 +/- 2, 280 +/- 4] mm yr(-1) for the northward, eastward and upward components, respectively, with respect to the stable interior of the South America Plate. The observed deformation cannot be explained by changes in the gravitational load caused by variations in the water level in the reservoir. For the most recent observation time interval, spanning 44 d in early 2012, the model that best fits the InSAR observations involves an inflating sill at a depth of 5.2 +/- 0.3 km, with length 9.0 +/- 0.3 km, width 5.3 +/- 0.4 km, dip 20 +/- 3 degrees from horizontal and strike 14 +/- 5 degrees clockwise from north, assuming a rectangular dislocation in a half-space with uniform elastic properties. During this time interval, the estimated rate of tensile opening is 1.1 +/- 0.04 m yr(-1), such that the rate of volume increase in the modelled sill is 51 +/- 5 million m(3) yr(-1) or 1.6 +/- 0.2 m(3) s(-1). From 2004 January to 2012 April the total increase in volume was at least 0.15 km(3) over the 5.2-yr interval observed by InSAR. The inflating region includes most of the 16-km-by-14-km ring of rhyolitic domes and coulees. The similarity of high-silica rhyolite compositions on opposite sides of the ring and the concentration of rhyolitic eruptions since similar to 20 ka suggest that processes within a large silicic magma chamber are responsible for the current deformation.