We report a novel phenomenon of chiral selection in self-assembled condensates of achiral amphiphiles. The handedness of chiral textures, reproducing the collective rotational component of the molecular orientation inside submillimeter circular domains, is correlated with the sign of a vortical stirring in the aqueous subphase. We propose an explanation based on the distinctive kinetics of topological defect annihilation during domain coalescence at the initial coarsening stage of a phase-separating monolayer.