A general-purpose rate-based algorithm for the construction of chemical kinetic models for systems with hundreds or thousands of reacting species is presented. The algorithm comprehensively works out the details of the chemistry implied by given reaction rate estimation rules, identifies the species and reactions that are numerically significant, and solves the resulting system of differential equations to compute the concentrations of the significant species as a function of time. A key innovation is a definition and numerical test for the "completeness" of the kinetic scheme. This approach obviates the need to arbitrarily neglect certain species and reactions in order to keep reaction schemes small enough to be manageable and allows chemical kinetic modelers to focus on the chemistry rather than on the computational details. Examples of hydrocarbon pyrolysis and combustion applications are presented, where the computer evaluates the importance of nearly 100 000 reactions in the process of identifying the few hundred species that are kinetically significant. The new algorithm, given reliable rate estimation rules, provides a framework for systematically constructing kinetic schemes including all of the numerically significant species, even for systems involving so many reactions that they could not be handled manually.