As interesting as jtp's question is, the answer, for the time being, doesn't actually include a common understanding of the definition of RNA. The substance (for lack of a more scientific term) responsible for success in some experiments is called a ribozyme. The ribozyme is a particular kind of primitive ribonuclic acid that could reproduce at least part of its self. "...primitive RNA molecules assembled themselves randomly from building blocks in the primordial ooze and accomplished some very simple chemical chores. But as far as anyone knew, RNA couldn't do anything but carry information from DNA to ribosomes.
That changed in the early 1980's, when two biochemists, Sidney Altman and Thomas Cech, discovered independently a kind of RNA that could edit out unnecessary parts of the message it carried before delivering it to the ribosome. Since RNA - ribonucleic acid - was acting like a type of protein known as an enzyme, Cech called his discovery a ribozyme. The two were awarded the Nobel Prize for Biochemistry in 1989." (Source: Origins of Life and the RNA World: Author, Jolane Abrams, Santa Cruz Science Writers' Cabal).
Let me add that problematic to this research is the assumption of a "primordial ooze", which is whole other discussion, no?