The first demonstration that macromolecules could be evolved in a test tube was reported twenty-five years ago. That breakthrough meant that billions of years of chance discovery and refinement could be compressed into a few weeks, and provided a powerful tool that now dominates all aspects of protein engineering. A challenge has been to extend this scientific advance into synthetic chemical space: to enable the directed evolution of abiotic molecules. The problem has been tackled in many ways. These include expanding the natural genetic code to include unnatural amino acids, engineering polyketide and polypeptide synthases to produce novel products, and tagging combinatorial chemistry libraries with DNA. Importantly, there is still no small-molecule analog of directed protein evolution, i.e. a substantiated approach for optimizing complex (≥ 10^9 diversity) populations of synthetic small molecules over successive generations. We present a key advance towards this goal: a tool for genetically-programmed synthesis of small-molecule libraries from large chemical alphabets. The approach accommodates alphabets that are one to two orders of magnitude larger than any in Nature, and facilitates evolution within the chemical spaces they create. This is critical for small molecules, which are built up from numerous and highly varied chemical fragments. We report a proof-of-concept chemical evolution experiment utilizing an outsized genetic code, and demonstrate that fitness traits can be passed from an initial small-molecule population through to the great-grandchildren of that population. The results establish the practical feasibility of engineering synthetic small molecules through accelerated evolution.