A Born-Oppenheimer direct dynamics simulation of the O+ + CH4 reaction dynamics at hyperthermal energies has been carried out with the PM3 (ground quartet state) Hamiltonian. Calculations were performed at various collision energies ranging from 0.5 to 10 eV with emphasis on high energy collisions where this reaction is relevant to materials erosion studies in low Earth orbit and geosynchronous Earth orbit. Charge transfer to give CH4+ is the dominant channel arising from O+ + CH4 collisions in this energy range, but most of the emphasis in our study is on collisions that lead to reaction. All energetically accessible reaction channels were found, including products containing carbon-oxygen bonds, which is in agreement with the results of recent experiments. After correcting for compensating errors in competing reaction channels, our excitation functions show quantitative agreement with experiment (for which absolute magnitudes of cross sections are available) at high collision energies (several eV). More detailed properties, such as translational and angular distributions, show qualitative agreement. The opacity function reveals a high selectivity for producing OH+ at high impact parameters, CH3+/CH2+/H2O+ at intermediate impact parameters, and H2CO+/HCO+/CO+ at small impact parameters. Angular distributions for CH3+/CH2+/OH+ are forward scattered at high collision energies which implies the importance of direct reaction mechanisms, while reaction complexes play an important role at lower energies, especially for the H2O+ product. Finally, we find that the nominally spin-forbidden product CH3+ + OH can be produced by a spin-allowed pathway that involves the formation of the triplet excited product CH3+ ((a) over tilde E-3). This explains why CH3+ can have a high cross section, even at very low collision energies. The results of this work suggest that the PM3 method may be applied directly to the study of O+ reactions with small alkane molecules and polymer surfaces.