Nucleic acids can form efficient hybrid catalysts for asymmetric catalysis upon binding of low‐molecular‐weight metal complexes. Up to now DNA has been the preferred nucleic acid component, while RNA was largely ignored. It is shown that despite RNA′s successful use in ribozymes, RNA is less suited for use in hybrid catalysts for asymmetric catalysis. A common dimethyl bipyridine copper complex does not form highly active and enantioselective hybrid catalysts with RNA due to the absence of synergistic effects between the copper complex and dsRNA.