This paper describes the coupling of BATS-R-US (Block Adaptive Tree Solar-wind Roe-type Upwind Scheme), a magnetohydrodynamics (MHD) code representing the Earth's global magnetosphere and its coupling to the ionosphere and solar wind, and the Rice Convection Model (RCM), which represents the inner magnetosphere and its coupling to the ionosphere. The MHD code provides a time-evolving magnetic field model for the RCM as well as continuously updated boundary conditions for the electric potential and plasma. The RCM computes the distribution functions of inner magnetospheric particles, including transport of inner plasmasheet and ring current particles by gradient/curvature drifts; it thus calculates more accurate inner magnetospheric pressures, which are frequently passed to the MHD model and used to nudge the MHD values. Results are presented for an initial run with the coupled code for the case of uniform ionospheric conductance with steady solar wind and southward interplanetary magnetic field (IMF). The results are compared with those for a run of the MHD code alone. The coupled-code run shows significantly higher inner magnetospheric particle pressures. It also exhibits several well-established characteristics of inner magnetospheric electrodynamics, including strong region-2 Birkeland currents and partial shielding of the inner magnetosphere from the main force of the convection electric field. A sudden northward turning of the IMF causes the ring current to become more nearly symmetric. The inner magnetosphere exhibits an overshielding (dusk-to-dawn) electric field that begins about 10 min after the northward turning reaches the magnetopause and lasts just over an hour.