Living organisms exhibit consistent homochirality. It is argued that the specific, binary choice made is not an accident but is a consequence of parity violation in the weak interaction expressed by cosmic irradiation. The secondary muons and pairs are spin- and magnetic moment- polarized and may introduce a small, net chiral preference when they interact electromagnetically or quantum mechanically with molecules that have made the transition to self-replication. Although this preference is likely to be very small, it may suffice to give a chirally-dominant outcome after billions of replications, especially if combined with chirally-unbiased conflict between the two choices. Examples of mechanisms that can manifest the three essential steps of polarization, preference and domination are presented and some variations and possible implications are discussed.