Researching the conditions for the emergence of life -- not necessarily as it is, but as it could be -- is one of the main goals of Artificial Life. Artificial Chemistries are one of the most important tools in this endeavour, as they allow us to investigate the process by which metabolisms capable of self-reproduction and -- ultimately -- of evolving, might have emerged. While previous work has shown promising results in this direction, it is still unclear which are the fundamental properties of a chemical system that enable emergent structures to arise. To this end, here we present an Artificial Chemistry based on Combinatory Logic, a Turing-complete rewriting system, which relies on a minimal set of possible reactions. Our experiments show that a single run of this chemistry starting from a tabula rasa state discovers with no external intervention a wide range of emergent structures, including autopoietic structures that maintain their organisation unchanged, others that grow recursively, and most notably, patterns that reproduce themselves, duplicating their number on each cycle. All of these structures take the form of recursive algorithms that acquire basic constituents from the environment and decompose them in a process that is remarkably similar to biological metabolisms.