We present InSAR observations of deformation due to an intrusion in the Eyjafjallaj¿kull volcano, Southern Iceland, in 1994. More than 15 cm of deformation in the line of sight (LOS) direction is detected in a series of interferograms spanning a micro-earthquake swarm occurring in June 1994. The location of the seismicity is more than 6 km offset compared to the area of inferred maximum surface uplift. Through an inversion scheme we find that a horizontal sill intrusion experiencing variable opening of up to 0.36 m agrees well with the deformation data. The total intrusion volume is 0.017 km3. The northern periphery of the modeled intrusion fits well with the area of recorded seismicity, indicating a close connection. Several processes may be responsible. Our preferred explanation is that the earthquakes are caused by opening of a narrow magma channel from depth, feeding the sill.