We present numerical simulations of nonlinear, three-dimensional, time-dependent, giant-cell stellar convection and magnetic field generation. The velocity, magnetic field, and thermodynamic variables satisfy the anelastic magnetohydrodynamic equations for a stratified, rotating, spherical shell of ionized gas. The interaction of rotation and convection produces a nonlinear transport of angular momentum that maintains a differential rotation in radius and latitude. At the surface, our simulated angular velocity peaks in the equatorial region in agreement with Doppler measurements of the solar surface rotation rate; below the surface, it decreases with depth in agreement with what is inferred from the rotational frequency splitting of solar oscillations. The interaction of rotation and convection also maintains left-handed helical fluid motions in the northern hemisphere and right-handed motions in the southern hemisphere. Magnetic fields are generated by the shearing and twisting effects of the differential rotation and helical motions and are destroyed by eddy diffusion. They in turn feedback onto the velocity and thermodynamic fields via the Lorentz force and Joule heating. Although we have not continued the computation long enough to simulate a complete magnetic cycle, our solutions demonstrate how the induced magnetic fields propagate away from the equator in the opposite direction inferred from themore » solar butterfly diagram. We suggest that, instead of operating in the turbulent convective region, the solar dynamo may be operating at the base of the convection zone where our simulated helicity has the opposite sign and a smaller amplitude.« less