We report the first detection of unrest at Socompa, Northern Chile, a stratovolcano which has recorded no eruptions since ~7,200 years ago. We measure deformation at and around Socompa using Interferometric Synthetic Aperture Radar (InSAR) observations between Jan 2018 and Oct 2021. We find that, whilst initially inactive, Socompa shows a steady uplift (17.5 mm/yr) from Dec 2019, independently recorded by near-field continuous Global Positioning System (GPS) data. The data can be fit with pressure increase in an ellipsoidal source region stretching from 1.9 to 9.5 km, with a volume change rate of ~5.8×106 m3/yr. Our observations of the onset of uplift preclude the possibility that a nearby Mw 6.8 deep intraslab earthquake on 3rd June 2020 triggered the unrest. The deformation signal we detect indicates the initiation of unrest at Socompa, after at least two decades without measurable deformation, and many thousands of years without volcanic activity.