The complexity of modern biological life has long made it difficult to understand how life could emerge spontaneously from the chemistry of the early earth. The key to resolving this mystery lies in the simplicity of the earliest living cells. Through our efforts to synthesize extremely simple artificial cells, we hope to discover plausible pathways for the transition from chemical evolution to Darwinian evolution. We view the two key components of a primitive cell as a self-replicating nucleic acid genome, and a self-replicating boundary structure. I will describe our recent finding of a simple and robust pathway for the coupled growth and division of a model primitive cell membrane. I will also discuss recent experimental progress towards the synthesis of self-replicating nucleic acids, and the implications of these experiments for our understanding of the origin of life.