An explanatory model for the emergence of evolvable units must display emerging structures that (1) preserve themselves in time (2) self-reproduce and (3) tolerate a certain amount of variation when reproducing. To tackle this challenge, here we introduce Combinatory Chemistry, an Algorithmic Artificial Chemistry based on a minimalistic computational paradigm named Combinatory Logic. The dynamics of this system comprise very few rules, it is initialized with an elementary tabula rasa state, and features conservation laws replicating natural resource constraints. Our experiments show that a single run of this dynamical system with no external intervention discovers a wide range of emergent patterns. All these structures rely on acquiring basic constituents from the environment and decomposing them in a process that is remarkably similar to biological metabolisms. These patterns include autopoietic structures that maintain their organisation, recursive ones that grow in linear chains or binary-branching trees, and most notably, patterns able to reproduce themselves, duplicating their number at each generation.