An automated computational mechanism-generation technique is applied to construct elementary-step chemical kinetic reaction models for the pyrolysis of methane at 1038 K and 0.58 atm. Under these conditions, the pyrolysis process is extremely complex and exhibits autocatalysis. The mechanism-generation approach constructs a detailed set of elementary reactions, retrieves or estimates required reaction rates and thermochemistry, and constructs a kinetic model that gives excellent agreement with experimental data for several species. Key to the success is a newly developed capability of the algorithm to identify pressure-dependent chemically activated reactions. A rate-based species-selection methodology is used to determine kinetically significant species, and the algorithm is demonstrated to identify critical low-concentration byproducts. Multistep chemically activated reactions involving the formation of cyclopentadiene and subsequent hydrogen atom production are found to be important reactions, agreeing with previous literature findings. The present work demonstrates that computer-generated kinetic models can quantitatively predict experimental behavior for conditions where reaction rate constants and thermochemistry are reasonably well established. Several topics are also presented that outline areas of ongoing research.