In 2004, Ohtomo and Hwang discovered that an electron gas is created at the interface between insulating LaAlO3 and SrTiO3 compounds. Here we show that the generation of a conducting electron gas is related to an orbital reconstruction occurring at the LaAlO3/SrTiO3 interface. Our results are based on extensive investigations of the electronic properties and of the orbital structure of the interface using x-ray absorption spectroscopy. In particular, we find that the degeneracy of the Ti 3d states is fully removed and that the Ti 3d xy levels become the first available states for conducting electrons.