The hypothesis that all life on earth traces back to a single common ancestor is a fundamental postulate in modern evolutionary theory. Yet, despite its widespread acceptance in biology, there has been comparatively little attention to formally testing this "hypothesis of common ancestry". We review and critically examine some arguments that have been proposed in support of this hypothesis. We then describe some theoretical results that suggest the hypothesis may be intrinsically difficult to test. We conclude by suggesting an approach to the problem based on the Aikaike information criterion.