Muon imaging has recently emerged as a powerful method to complement standard geophysical tools in the understanding of the Earth's subsurface. Muon measurements yield a “radiography” of the average density along the muon path, allowing to image large volumes of a geological body from a single observation point. Here we jointly invert muon data from three simultaneous telescope acquisitions together with gravity data to estimate the three‐dimensional density structure of the La Soufrière de Guadeloupe lava dome. Our unique data set allows us to achieve an unprecedented spatial resolution with this novel technique. The retrieved density model reveals an extensive, low‐density anomaly where the most active part of the volcanic hydrothermal system is located, supporting previous studies that indicate this region as the most likely to be involved in a partial edifice collapse. Key Points We simultaneously image the La Soufrière de Guadeloupe lava dome with three muon telescopes aiming at the volcano from different locations We jointly invert the multitelescope muon data with gravity data to retrieve the three‐dimensional density distribution in the dome We find a low‐density, mechanically weak region where the hydrothermal system is most active, suggestive of an edifice collapse hazard