With the implementation of efficient algorithms for the accurate calculation of reaction source terms, computational fluid dynamics (CFD) is now a powerful tool for the simulation and design of chemical reactors with complex kinetic schemes. The example studied in this work is the methane chlorination reaction for which the detailed chemistry scheme has 152 reactions and 38 species. The adiabatic, jet-stirred chlorination reactor used for the CFD simulations is an insulated right cylinder with a coaxial premixed feed stream at one end. In order for this reactor to remain lit, recirculation of hot products is crucial, and hence, reactor stability is sensitive to both macroscale and microscale mixing. By neglecting density variations, a Lagrangian composition probability density function (PDF) code with a novel chemistry tabulation algorithm (in-situ adaptive tabulation or ISAT) for handling complex reactions is used to simulate the species concentrations and temperature field inside of the reactor. In addition, a reduced mechanism with 21 reactions and 15 species is tested for accuracy against the detailed chemistry scheme, a simplified CSTR model is used to illustrate the shortcomings of zero-dimensional models, and a pair-wise mixing stirred reactor (PMSR) model is used to show the stabilizing effect of micromixing on reactor stability. The CFD simulations are generally in good agreement with results from pilot-scale reactors for the outlet temperature and major species.