The thriving interest in the study of nanostructured materials is driving an ever increasing demand for experimental techniques that provide chemical information with very high spatial resolution. The ability to probe the nanoscale spectroscopically is needed in various fields, e.g. in the investigation of quantum-confined nanostructures such as Quantum Dots1, whose electronic properties are often determined by nanoscale chemical inhomogeneities. X-ray Photoemission Electron Microscopy (XPEEM) with high lateral resolution should be regarded among the best suited available tools for an experimentally convenient, minimally intrusive, direct inspection of the elemental composition of surfaces in the nanorange. Nonetheless a quantitative and reliable exploitation of XPEEM - while most desirable - is extremely challenging2. Here we demonstrate the possibility to quantify the elemental content of surfaces at the few-percent level and with lateral resolution better than ~50 nm by in situ XPEEM. We show chemical maps of the surface of Stranski-Krastanov-grown germanium/silicon islands on (111)-oriented silicon substrates3, a system of deep scientific interest and special potential for applications in the micro- and opto- electronics4,5. Our insight provides a novel and most precious perspective on the dynamics of growth and alloying in the heteroepitaxy of semiconductors, along with the experimental database for understanding the electronic behavior of individual nanostructures. These achievements bring to fruition the full power of XPEEM under the particular conditions of binary alloys with a morphology mapped a priori. In view of a comprehensive extension of the scope and reach of our method, we will demonstrate a progressive route towards the quantitative chemical mapping of arbitrarily complex surfaces by spectromicroscopy. Immediate developments of our approach will aim at the non-destructive characterization of strain gradients at the nanoscale, another key and urgent challenge for the community involved in materials science and technology. 1 A.P. Alivisatos, Science 271, 933 (1996). 2 F. Ratto, F. Rosei, A. Locatelli, S. Cherifi, S. Fontana, S. Heun, P.D. Szkutnik, A. Sgarlata, M. De Crescenzi, N. Motta, J. Appl. Phys. 2005, 97, 043516. 3 F. Ratto, A. Locatelli, S. Fontana, S. Kharrazi, S. Ashtaputre, S.K. Kulkarni, S. Heun, F. Rosei, Small 2006, 2, 401. 4 F.M. Ross, R.M. Tromp, M.C. Reuter, Science 1999, 286, 5446. 5 F. Rosei, J. Phys.: Condens. Matter 2004, 16, 1373.