A modified Chapman—Enskog technique developed for a partially ionized gas in an electric field is generalized to include the effects of a magnetic field. The method allows the electron and heavy particle temperatures to differ while requiring all species to have the same macroscopic velocity to zero order. Expressions are obtained for the transport properties of such a gas and a complete set of self‐contained magnetohydrodynamic equations is given. As an example, the transport properties of a fully ionized gas containing a single ion species are evaluated using the cutoff Coulomb potential. In the limit of equal electron and ion temperatures, the results are in agreement with previous results.