We invert Rayleigh waves reconstructed from cross-correlations of 18 months of ambient seismic noise recorded by permanent seismological stations run by the Piton de la Fournaise Volcanological Observatory. By correlating noise records between 21 receivers, we reconstruct Rayleigh waves with sufficient signal-to-noise ratio for 210 inter-station paths. We use the reconstructed waveforms to measure group velocity dispersion curves at periods between 1.5 and 4.5 s. The obtained measurements are inverted for two-dimensional group velocity maps and finally for a 3-D S-wave velocity model of the edifice from +2 to -1 km above sea level. Our results clearly show a high velocity body spatially delimited by the borders of the active 10 km wide caldera. The preferential N30¿-N130¿ orientations of this anomaly at -0.5 km below sea-level is an evidence of the preferential paths of magma injections associated to the NE-SE Rift Zones. This structure is surrounded by a low-velocity ring interpreted as effusive products associated to the construction of the Piton de la Fournaise volcano on the flank of the older Piton des Neiges volcano.