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We have investigated the surface chemical composition of crystalline films of La0.65Sr0.35MnO3 by angle-resolved x-ray photoelectron spectroscopy. The surface composition was found to be significantly different from that of the bulk because of an appreciable Sr segregation. Furthermore, our study suggests that this Sr segregation has caused a major restructuring of the surface region characterized by the formation of a Ruddlesden-Popper phase (La,Sr)n+1MnnO3n+1 with n = 1. Segregation and restructuring in the surface region should be common in these doped perovskites and will have a profound impact on the electronic and magnetic properties of ultrathin films and magnetic tunneling junctions made of these materials.