A drawback of high-quality modes in optical microdisks is their isotropic light emission characteristics. Here we report a novel, robust, and general mechanism that results in highly directional light emission from those modes. This surprising finding is explained by a combination of wave phenomena (wave localization along unstable periodic ray trajectories) and chaotic ray dynamics in open systems (escape along unstable manifolds). The emission properties originating in the chaotic ray dynamics permit directional light output even from microlasers operating in the common multi-mode regime. We demonstrate our novel mechanism for the limacon billiard family and find directional emission with narrow angular divergence for a significant range of geometries and material parameters.