Here we report lasing action in limac{c}on-shaped GaAs microdisks with quantum dots (QDs) embedded. Although the intracavity ray dynamics is predominantly chaotic, high-$Q$ modes are concentrated in the region $chi > chi_c$ as a result of wave locali
zation. Strong optical confinement by total internal reflection leads to very low lasing threshold. Our measurements show that all the lasing modes have output in the same direction, regardless of their wavelengths and intracavity mode structures. This universal emission direction is determined by directed phase space flow of optical rays in the open chaotic cavity. The divergence angle of output beam is less than 40 degree. The unidirectionality proves to be robust against small deviations of the real cavity shape and size from the designed values.
