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Life is confronted with computation problems in a variety of domains including animal behavior, single-cell behavior, and embryonic development. Yet we currently do not know of a naturally existing biological system that is capable of universal computation, i.e., Turing-equivalent in scope. Generic finite-dimensional dynamical systems (which encompass most models of neural networks, intracellular signaling cascades, and gene regulatory networks) fall short of universal computation, but are assumed to be capable of explaining cognition and development. I present a class of models that bridge two concepts from distant fields: combinatory logic (or, equivalently, lambda calculus) and RNA molecular biology. A set of basic RNA editing rules can make it possible to compute any computable function with identical algorithmic complexity to that of Turing machines. The models do not assume extraordinarily complex molecular machinery or any processes that radically differ from what we already know to occur in cells. Distinct independent enzymes can mediate each of the rules and RNA molecules solve the problem of parenthesis matching through their secondary structure. In the most plausible of these models all of the editing rules can be implemented with merely cleavage and ligation operations at fixed positions relative to predefined motifs. This demonstrates that universal computation is well within the reach of molecular biology. It is therefore reasonable to assume that life has evolved - or possibly began with - a universal computer that yet remains to be discovered. The variety of seemingly unrelated computational problems across many scales can potentially be solved using the same RNA-based computation system. Experimental validation of this theory may immensely impact our understanding of memory, cognition, development, disease, evolution, and the early stages of life.