The combination of a gaseous core fission reactor with a magnetohydrodynamic (MHD) generator can lead to more efficient conversion of fission energy to electricity than can conventional conversion systems. A system concept currently being investigated utilizes uranium tetrafluoride (UF4) as fuel and potassium or potassium fluoride (KF) as the working fluid. The electrical conductivity of the gas greatly influences the performance of the MHD generator. It is possible to enhance the electrical conductivity by taking advantage of fission fragment ions born in the fissile gas-working gas mixture. To study and quantify this effect, a chemical reaction model as well as a physical model are developed. The governing rate equations and an electron energy balance equation are numerically solved for steady-state and spatially homogeneous cases. The electrical conductivity of a UF4-K/KF gaseous mixture is shown to be a function of neutron flux at representative gas conditions (2500 K and 1 atm). The enhancement is achieved because of the rise in electron temperature due to fission fragment heating.