A method for constructing a variety of probabilistic lattice-gas cellular automata for chemically reacting systems is described. The microscopic reactive dynamics give rise to a general fourth-order polynomial rate law for the average particle density. The reduction of the microdynamical equations to a discrete or continuous Boltzmann equation is presented. Connection between the linearized Boltzmann equations and a reaction-diffusion macroscopic equation is discussed. As an example of the general formalism a set of cellular automata rules that yield the Schlogl phenomenological model is constructed. Simulation results are presented. © 1990 The American Physical Society.