A key question in origin-of-life research is how primitive life or life-like systems obtained reusable and reprogrammable machineries of processing information to respond to various environmental and internal stimuli. One strategy to approach this question is viewing living systems as universal chemical computers. This approach focuses upon uncovering how reusable and reprogrammable chemical NOT, AND, and OR logic gates could appear under prebiotically possible scenarios where simple chemicals and second- or lower-order reactions are more frequent than macromolecules and higher-order reactions. Here, we model two theoretical mechanisms of forming Boolean gates based on geochemically plausible reaction systems that could have preceded complex biopolymers. The mechanisms exploit simple bistable autocatalytic systems to encode binary variables and use heterogeneous dilution rates to differentially activate or deactivate autocatalysis in different reactors. We found that NOT, AND, and OR gates, as well as more complex logic circuits, can spontaneously arise from connected, well-mixed flow reactors based on (i) catalysis by a heterodimer between mutually inhibitory autocatalysts or (ii) selectively permeable tunnels connecting reactors. Our results suggest that the prebiotic emergence of chemical logic circuits provides new guides for experimentally actualizing chemical computation.