The inversion of methane bound to first-row transition-metal ions from Sc+ to Cu+ is systematically investigated using the B3LYP method, a hybrid density-functional-theory method of Becke and Lee, Yang, and Parr. The computed transition states for the methane inversion on the M+(CH4) complexes have a C-s structure in which one pair of C-H bonds is about 1.2 Angstrom in length and the other pair is about 1.1 Angstrom. The barrier height for the methane inversion is significantly decreased from 109 kcal/mol for free methane to 43-48 kcal/mol on the late transition-metal complexes, Fe+(CH4), Co+(CH4), Ni+(CH4), and Cu+(CH4). Since each activation energy involves the binding energy of the complex (16 kcal/mol on the average), the actual barrier height should be lower by this quantity if measured from the dissociation limit. The inversion of methane can therefore occur at the transition-metal active center of catalysts or enzymes under ambient conditions through a thermally accessible transition state, and it would reasonably lead to inversion of stereochemistry at a carbon atom in catalytic reactions of hydrocarbons. We propose that a radical mechanism based on a planar carbon species may not be the sole source of the observed loss of stereochemistry in transition-metal-catalyzed hydrocarbon hydroxylations and other related reactions.