We present a structural determination of the surface reconstruction of the Sm(0001) surface using surface x-ray diffraction, scanning tunneling microscopy, and ab initio calculations. The reconstruction is associated with a large (22%) expansion of the atomic radius for the top monolayer surface Sm atoms. The mechanism driving the surface reconstruction in Sm is unique among all elements and is connected to the strong correlations of the 4f electrons in Sm and the intermediate valence observed in certain Sm compounds. The atoms constituting the top monolayer of Sm(0001) have vastly different chemical properties compared to the layer underneath and behave as if they were an adsorbate of a different chemical species.