We investigate the electronic properties of the LaAlO3/SrTiO3 interface using density functional theory. In contrast to previous studies, which relied on (semi-)local functionals and the GGA+U method, we here use a recently developed hybrid functional to determine the electronic structure. This approach offers the distinct advantage of accessing both the metallic and insulating multilayers on a parameter-free equal footing. As compared to calculations based on semilocal GGA functionals, our hybrid functional calculations lead to a considerably increased band gap for the insulating systems. The details of the electronic structure show substantial deviations from those obtained by GGA calculations. This casts severe doubts on all previous results based on semilocal functionals. In particular, corrections using rigid band shifts (“scissors operator”) cannot lead to valid results.