The single-handedness of biological molecules is critical for molecular recognition and replication processes and would seem to be a prerequisite for the origin of life. A drawback of recently reported synthetic routes to RNA is the requirement for enantioenriched reactants, which fails to address the puzzle of how the single chirality of biological molecules arose. Here, we report the synthesis of highly enantioenriched RNA precursor molecules from racemic starting materials, with the molecular asymmetry derived solely from a small initial imbalance of the amino-acid enantiomers present in the reaction mixture. Acting as spectators to the main reaction chemistry, the amino acids orchestrate a sequence of physical and chemical amplification processes. The emergence of molecules of single chirality from complex, multi-component mixtures supports the robustness of this synthesis process under potential prebiotic conditions and provides a plausible explanation for the single-handedness of biological molecules before the emergence of self-replicating informational polymers.