The "RNA world" hypothesis proposes that early in the evolution of life, before the appearance of DNA or protein, RNA was responsible both for encoding genetic information and for catalyzing biochemical reactions. Ribo-organisms living in the RNA world would have replicated their RNA genomes by using an RNA polymerase ribozyme. Efforts to provide experimental support for the RNA world hypothesis have focused on producing such a polymerase, and in vitro evolution methods have led to the isolation of a polymerase ribozyme that catalyzes primer extension which is accurate and general, but slow. To understand the reaction of this ribozyme, we developed a method of measuring polymerase processivity that is particularly useful in the case of an inefficient polymerase. This method allowed us to demonstrate that the polymerase ribozyme, despite its inefficiency, is partially processive. It is currently limited by a low affinity for the primer-template duplex, but once it successfully binds the primer-template duplex in the productive alignment, it catalyzes an extension reaction that is so rapid that it can occur multiple times during the short span of a single binding event. This finding contributes to the understanding of one of the more sophisticated activities yet to be generated de novo in the laboratory and sheds light on the parameters to be targeted for further optimization.