  Here we report lasing action in lima\c{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 localization. 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.
