Slow earthquakes and afterslips prove that the Earth does not have just two response time scales, i.e. that of tectonic loading and that of regular earthquakes. A swarm of slow earthquakes, with time constants of the order of hundreds of seconds, has been detected by a laser interferometer below the Gran Sasso massif (Italy). We analyse and model these observations to identify a very plausible source in a local fault, with no historic seismic behavior. While slow earthquakes occurring in subduction zones, and at the transition between locked and stably sliding segments of the San Andreas fault, are often associated with seismic events, in the case of the Apennines there is no correlation between local seismicity and slow earthquakes. Slow earthquakes, therefore, may also represent a specific failure behavior for a seismically locked fault, adding further complexity to the interpretation of geologic data for seismic hazard estimates.