Dr. Sarah Voytek and a group of researchers at the Scripps Research Institute has observed the evolution of self-catalysing RNA molecules in vitro.
These non-living molecules have the ability to self replicate, but do so imperfectly. In so doing, they use resources for building blocks and for energy. By placing different molecules in the same test tube of nutrients, they observed both evolution of the molecules (those more able to use the resources produced more copies) and resource partitioning (when competing for the same limited resources, they would specialize to different specific resources).
This experiment demonstrates the probabilistic nature of selection, and confirms that any self-replicating system, including non-living ones, can evolve. It also, once again, demonstrates the predictive power (and hence correctness) of Natural Selection.