We present a novel unit of evolution: a self-reproducing cell in a two-dimensional artificial chemistry. The cells have a strip of genetic material that is used to produce enzymes, each catalyzing a specific reaction that may affect the survival of the cell. The enzymes are kept inside the cell by a loop of membrane, thus ensuring that only the cell that produced them gets their benefit. A set of reaction rules, each simple and local, allows the cells to copy their genetic information and physically divide. The evolutionary possibilities of the cells are explored, and it is suggested that the system provides a useful framework for testing hypotheses about self-driven evolution.