The crucial role of homochirality and chiral homogeneity in the self-replication of contemporary biopolymers is emphasized, and the experimentally demonstrated advantages of these chirality attributes in simpler polymeric systems are summarized. The implausibility of life without chirality and hence of a biogenic scenario for the origin of chiral molecules is stressed, and chance and determinate abiotic mechanisms for the origin of chirality are reviewed briefly in the context of their potential viability on the primitive Earth. It is concluded that all such mechanisms would be nonviable, and that the turbulent prebiotic environment would require an ongoing extraterrestrial source for the accumulation of chiral molecules on the primitive Earth. A scenario is described wherein the circularly polarized ultraviolet synchrotron radiation from the neutron star remnants of supernovae engenders asymmetric photolysis of the racemic constituents in the organic mantles on interstellar dust grains, whereupon these chiral constituents are transported repetitively to the primitive Earth by direct accretion of the interstellar dust or through impacts of comets and asteroids.