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In astronomy there are basically four kinds of observations to extract the information carried by electromagnetic radiation: photometry, imaging, spectroscopy, and polarimetry. By optimal exploitation of the first three techniques, X-ray astronomy has been able to unveil the violent world of compact high-energy sources. Here, we report on a new instrument that brings high efficiency also to X-ray polarimetry, the last unexplored field of X-ray astronomy. It will then be possible to resolve the internal structures of compact objects, which otherwise would remain inaccessible even to X-ray interferometry. The new instrument derives the polarization information from the track of the photoelectron imaged by a finely subdivided gas pixel detector. Its great improvement of sensitivity (at least two order of magnitude) will allow direct exploration of the most dramatic objects of the X-ray sky.