It is proposed that nucleotide strands of opposite handedness may strongly associate and thereby provide the key step of a mechanism for the amplification of a small enantiomeric excess in an initially near-racemic mixture of poly- or oligonucleotides. This hypothesis, if confirmed by experimentation, may have important implications for the question of the origin of biomolecular chirality. The results of preliminary NMR experiments are given, which do show evidence of a strong association between pentanucleotide RNA strands whose monomers have opposite chirality. Simple kinetic equations are solved to demonstrate the conditions under which such association can produce amplification of chirality.