We present results from a global 3-D nonlinear simulation of magnetic dynamo action achieved by solar convection in a penetrative geometry. We include within the spherical computational domain both the bulk of the convection zone and a portion of the underlying stable layer. A tachocline of rotational shear is realized below the convection zone, where we have imposed both a hydrodynamic drag term and small thermal perturbations consistent with thermal wind balance. Thus we are capturing many of the dynamical elements thought to be essential in the operation of the global solar dynamo, including differential rotation arising from convection, magnetic pumping, and the stretching and amplification of toroidal fields within the tachocline. In the stable region, the simulation reveals that strong axisymmetric toroidal magnetic fields (about 3000 G in strength) are realized, in contrast to the mostly fluctuating fields that predominate in the convection zone. The toroidal fields in the stable region exhibit a striking antisymmetric parity akin to that observed in sunspots, with fields in the northern hemisphere largely of the opposite sign to those in the southern hemisphere. These deep toroidal fields are accompanied by mostly dipolar mean poloidal fields, whose polarity has retained the same sense over multiple years of simulated evolution.