Observations of microseismicity provide a powerful tool for mapping the movement of melt in the crust. Here we record remarkable sequences of earthquakes 20 km below the surface in the normally ductile crust in the vicinity of Askja Volcano, in northeast Iceland. The earthquakes occur in swarms consisting of identical waveforms repeating as frequently as every 8 s for up to 3 h. We use template waveforms from each swarm to detect and locate earthquakes with an automated cross-correlation technique. Events are located in the lower crust and are inferred to be the result of melt being injected into the crust. During melt intrusion high strain rates are produced in conjunction with high pore fluid pressures from the melt or exsolved carbon dioxide. These cause brittle failure on high-angle fault planes located at the tips of sills. Moment tensor solutions show that most of the earthquakes are opening cracks accompanied by volumetric increases. This is consistent with the failure causing the earthquakes by melt injection opening new tensile cracks. Analysis of the magnitude distribution of earthquakes within a swarm reveals a complicated relationship between the imposed strain rates and the fluids that cause brittle failure. The magnitude of the earthquakes is controlled by the distance fluids can migrate along a fault, whereas the frequency of the events is controlled by the strain rate. Faults at the tips of sills act to focus melt transport between sills and so must be an important method of transporting melt through the lower crust.