A new scenario for prebiotic formation of nucleic acid oligomers is presented. Peptide catalysis is applied to achieve condensation of activated RNA monomers into short RNA chains. As catalysts, L-dipeptides containing a histidine residue, primarily Ser-His, were used. Reactions were carried out in selforganised environment, a water-ice eutectic phase, with low concentrations of reactants. Incubation periods up to 30 days resulted in the formation of short oligomers of RNA. During the oligomerisation, an active intermediate (dipeptide–mononucleotide) is produced, which is the reactive species. Details of the mechanism and kinetics, which were elucidated with a set of control experiments, further establish that the imidazole side chain of a histidine at the carboxyl end of the dipeptide plays a crucial role in the catalysis. These results suggest that this oligomerisation catalysis occurs by a transamination mechanism. Because peptides are much more likely products of spontaneous condensation than nucleotide chains, their potential as catalysts for the formation of RNA is interesting from the origin-of-life perspective. Finally, the formation of the dipeptide–mononucleotide intermediate and its significance for catalysis might also be viewed as the tell-tale signs of a new example of organocatalysis.