The Hengill triple junction, at the western end of the Southern Iceland seismic zone (SISZ), exhibits the highest level of continuous seismicity in Iceland. In July 1994, an unusually persistent swarm of earthquakes, with magnitude less than 4, continued through 1995 with intermittent activity through 1999. This seismicity appears to be mechanically coupled to the ongoing volcanic activity. To study this coupling, we measure crustal deformation using interferometric analysis of synthetic aperture radar (INSAR) images acquired by the Earth Resources Satellites ERS-1 and ERS-2 of the European Space Agency. This technique provides dense (100 pixels/km2) spatial coverage and monthly sampling in the summer months between 1993 and 1998. The resulting interference patterns show clear fringes, even after four years, on the barren ground cover near the Hengill central volcano. The radar coherence breaks down, however, in less than a month in the coastal lowlands containing most of the active faults of the SISZ. The principal signal in the interferograms is a concentric pattern with radius of approximately 10 km, centered on Hrómundartindur volcano. These fringes indicate a relative shortening of the radar line-of-sight distance (range) of approximately 1.5 cm/year. We intepret this signature as mostly vertical uplift due to increasing pressure in a magma chamber at depth. To explain it, we employ a simple "Mogi" model of a point source in an elastic half space. After estimating the four parameters of this model for each of the 10 observed interferograms, we find that the rate of uplift is constant, with an average value of 192 mm/year from 1993 through 1998. The best fitting models locate the point source at a depth of 72 km depth at 64.032/circN and 21.213/circW. The constant rate of volcanic deformation contrasts markedly with the episodic moment release by swarms or "crises" of earthquakes. To explain this contrast, we propose that the ongoing volcanic activity increases the stress in the brittle country rock. When the stress reaches the Coulomb failure threshold, the rock breaks, rupturing a fault and releasing the stress (Figure 14).