Arc volcanoes are underlain by complex systems of molten-rock reservoirs ranging from melt-poor mush zones to melt-rich magma chambers. Petrological and satellite data indicate that eruptible magma chambers form in the topmost few kilometres of the crust. However, very few chambers have ever been definitively located, suggesting that most are too short-lived or too small to be imaged, which has direct implications for hazard assessment and modelling of magma differentiation. Here we use a high-resolution technology based on inverting full seismic waveforms to image a small, high-melt-fraction magma chamber that was not detected with standard seismic tomography. The melt reservoir extends from ~2 to at least 4 km below sea level (b.s.l.) at Kolumbo – a submarine volcano near Santorini, Greece. The chamber coincides with the termination point of the recent earthquake swarms and may be a missing link between a deeper melt reservoir and the high-temperature hydrothermal system venting at the crater floor. The chamber poses a serious hazard as it could produce a highly explosive, tsunamigenic eruption in the near future. Our results suggest that similar reservoirs (relatively small but high melt-fraction) may have gone undetected at other active volcanoes, challenging the existing eruption forecasts and reactive-flow models of magma differentiation.