In this thesis, a minimal artificial chemistry system is presented, which is inspired by the RNA World hypothesis and is loosely based on Holland's Learning Classier Systems. The Molecular Classier System (MCS) takes a bottom-up, individual-based approach to building artificial bio-chemical networks. The MCS has been developed to demonstrate the effects of hierarchical selection. Hierarchical selection appears to have been critical for the evolution of complexity in life as we know it yet, to date, no computational artificial life system has investigated the viability of using hierarchical selection as a mechanism for achieving qualitatively similar results. Hierarchy in MCS is enforced by constraining artificial molecules, which are modeled as individuals, to exist within externally provided containers - protocells. This research is focused on the period of time surrounding the conjectured first Major Transition - from individual replicating molecules to populations of molecules existing within cells. Protocells can be thought of as simplified versions of contemporary biological cells. Molecular replication within these protocells causes them to grow until they undergo a process of binary fission. Darwinian selection is continuously and independently applied at both the molecular level and the protocell level. Experimental results are presented which display the phenomenon of selectional stalemate where the selectional pressures are applied in opposite directions such that they meet in the middle. The work culminates with the presentation of a stable artificial protocell system which is capable of demonstrating ongoing evolution at the protocell level via hierarchical selection of molecular species. Supplementary results are presented in the Appendix material as a set of experiments where selectional pressure is applied at the protocell level in a manner that indirectly favours particular artificial bio-chemical networks at the molecular level. It is shown that a molecular trait which serves no useful purpose to the molecules when they are not contained within protocells is exploited for the benefit of the collective once the molecules are constrained to live together. It is further shown that through the mechanism of hierarchical selection, the second-order effects of this molecular trait can be used by evolution to distinguish between protocells which contain desirable networks, and those that do not. A treatment of the computational potential of such a mechanism is presented with special attention given to the idea that such computation may indeed form the basis for the later evolution of the complicated Cell Signaling Pathways that are exhibited by modern cells.