In this paper, a novel concept of a leaky-wave antenna is proposed, based on the use of Huygens metasurfaces. It consists of a parallel-plate waveguide in which the top plate is replaced by a bianisotropic metasurface of the Omega type. It is shown that there is an exact solution to transform the guided mode into a leaky-mode with arbitrary control of the constant leakage factor and the pointing direction. Although the solution turns out to be periodic, only one Floquet mode is excited and radiates, even for electrically long periods. Thanks to the intrinsic spurious Floquet mode suppression, broadside radiation can be achieved without any degradation. Simulations with idealized reactance sheets verify the concept. Moreover, physical structures compatible with PCB fabrication have been proposed and designed, considering aspects such as the effect of losses. Finally, experimental results of two prototypes are presented and discussed.