Debris avalanches derived from the flanks of volcanic islands are among the largest on Earth. Debris avalanches are rare, catastrophic destabilizations that still keep geologists debating about the mechanisms that initiate them and make them travel huge runout distances. To shed light on the trigger of such destabilizations, we studied the inland scar of a debris avalanche deposit cropping out at Piton des Neiges, a dormant and eroded basaltic volcano of La Réunion Island. The avalanche deposit rests on a pile of 50-70 sill intrusions with a shallow northward dip, i.e. toward the sea. We measured the anisotropy of magnetic susceptibility in a transect across the uppermost sill of the pile in contact with the avalanche deposit. This transect reveals a strongly asymmetric magnetic fabric, consistent with a north-directed shear movement of the upper intrusion wall. This suggests that the upper sill induced a co-intrusive shear displacement of the volcano flank toward the sea. The upper sill margin in contact with the avalanche is striated, showing that this intrusion is older than the avalanche. Striae indicate a northward direction of avalanche runout. The upper sill margin also displays a magmatic lineation consistent with a magma flow in the intrusion toward the north. There is thus a striking kinematic consistency between the directions of intrusion propagation and avalanche runout, both oriented toward the sea. From the above results, we propose that repeated sill intrusions, such as observed on Piton des Neiges, increase the instability of a volcanic edifice. Each injection induces an incremental slip of the overlying rock mass, which may eventually end up into a landslide. Sill intrusions associated with seaward displacements of volcano flank, such as inferred for the April 2007 eruption of Piton de la Fournaise (also in La Réunion), should therefore be considered as a potential trigger of debris avalanches.