Noise added to a chirally autocatalytic model system is usually known to cause mirror-symmetry breaking with statistically equal distributions for the two product enantiomers. We show that if such a system is asymmetrically perturbed by means of a very small undetectable bias in the racemization equilibrium between the two enantiomers, adding Gaussian white noise can lead to an efficient enantioselection. Consequently, within a certain range of the noise amplitude, symmetry breaking gives rise to an entirely biased statistical distribution in favor of one of the enantiomers. In contrast, racemic results will be obtained for the corresponding deterministic case (in the absence of noise). Thus, added noise plays a constructive role by directing the chiral system into a specific enantiomeric direction while being influenced only by a subthreshold asymmetric input. This effect could be of conceptual interest for the impact of weak asymmetric fields on nonlinear chemical reactions.