A superglass is a phase of matter which is characterized at the same time by superfluidity and a frozen amorphous structure. I will introduce a model of interacting bosons in three dimensions that displays this phase unambiguously and that can be analyzed exactly or using controlled approximations. Employing a mapping between quantum Hamiltonians and classical Fokker-Planck operators, the ground state wavefunction of the quantum model is proportional to the Boltzmann measure of classical hard spheres. This connection allows to obtain quantitative results on static and dynamic quantum correlation functions. In particular, by translating known results on the glassy dynamics of Brownian hard spheres one can work out the properties of the superglass phase and of the quantum phase transition between the superfluid and the superglass phase.