Tectonic activity in the Hengill volcanic area in southwestern Iceland accelerated in July 1994, when an unusually persistent swarm of moderate-sized earthquakes began. Although the largest events were magnitude 5, the pattern of upward crustal deformation at 2 cm/yr indicates that most of the activity is related to inflation of a magma chamber at depth. To monitor this activity, we analyze synthetic aperture radar (SAR) images acquired by the ERS-1 and ERS-2 satellites between July 1993 and September 1998 using interferometry. Interferograms composed of images acquired during the snow-free summer months remain coherent on Holocene lava flows, even after 4 years. Some of the interferograms show a discontinuity in the fringe pattern, which we interpret as 8 mm of (aseismic) dip slip on a 3-km-long segment of a N5 ¿E striking normal fault, part of which had been mapped previously. This slip must have occurred between July 31 and September 3, 1995 (inclusive), and has been confirmed by observations in the field. The predominant signature in all the interferograms spanning at least 1 year, however, is a concentric fringe pattern centered just south of the Hr¿mundartindur volcanic center. This we interpret as mostly vertical uplift caused by increasing pressure in an underlying magma source. The volume source that best fits the observed interferograms lies at 7¿1 km depth and remains in the same horizontal position to within 2 km. It produces 19¿2 mm/yr of uplift. This deformation accumulates as elastic strain energy at a rate 2.8 times the rate of seismic moment release. Accumulated over 5 years, it increases the Coulomb failure stress by >0.6 bar in an area that includes some 84% of the earthquakes recorded between 1993 and 1998. Under our interpretation, magma is injected at 7 km depth, just below the seismogenic zone formed by colder, brittle rock. There the inflation induces stresses that exceed the Coulomb failure criterion, triggering earthquakes, possibly in a cyclical fashion. ¿ 2001 American Geophysical Union