Interesting question - look up RNA world hypothesis. In short it postulates that the most likely first biomolecule to exist and auto replicate was in fact RNA/Ribozymes as it is able to independently replicate, catalyse simple chemical reactions and interact with its environment under certain forms.

This is what we call autocatalytic RNA or a Ribozyme. This idea has even been tested in the lab, and they have been able to guide the evolution of autocatalytic RNA to make it more and more prone to auto replication - eventually it just starts evolving itself and producing new features through mutation which may or may not favour survival.

Check out this article from Science for more information: http://science.sciencemag.org/content/323/5920/1436.full