Singlet Orbital Ordering in Bilayer Sr_{3}Cr_{2}O_{7}.

We perform an extensive study of Sr_{3}Cr_{2}O_{7}, the n=2 member of the Ruddlesden-Popper Sr_{n+1}Cr_{n}O_{3n+1} system. An antiferromagnetic ordering is clearly visible in the magnetization and the specific heat, which yields a huge transition entropy, Rln(6). By neutron diffraction as a function of temperature we have determined the antiferromagnetic structure that coincides with the one obtained from density functional theory calculations. It is accompanied by anomalous asymmetric distortions of the CrO_{6} octahedra. Strong coupling and Lanczos calculations on a derived Kugel-Khomskii Hamiltonian yield a simultaneous orbital and moment ordering. Our results favor an exotic ordered phase of orbital singlets not originated by frustration.