Any large-scale magnetic fields present in solar/stellar radiative interiors have so far been thought to be primordial or residuals from extinct dynamos. We show that a regular cyclic dynamo can also be the origin of strong magnetic fields in the solar radiative tachocline and interior below. By exploiting a kinematic, mean-field flux-transport dynamo, we show that for a wide range of core-diffusivity values, from 10~9 cm~2 s~(-1) down to a molecular diffusivity of 10~3 cm~2 s~(-1), oscillatory dynamo fields penetrate below the tachocline. Amplitudes of these fields are in the range of ～1 kG to 3 x 10~3 kG, depending on core diffusivity value, when the dynamo produces ～100 kG peak toroidal fields in the overshoot tachocline. For a low enough core diffusivity (approx < 10~7 cm~2 s~(-1)), there is also a steady (nonreversing) dynamo in the radiative tachocline and below, which generates strong toroidal field of amplitude ～1 kG to 3 x 10~3 kG or more there. The key elements in this dynamo are the low diffusivity, the differential rotation near the bottom of the tachocline, and an assumed tachocline α-effect. The Lorentz force feedback may limit oscillatory dynamo fields to ～30 kG, for which the mean nonreversing toroidal fields is still ～300 kG, for the lowest core diffusivity value. The presence of strong oscillatory and steady toroidal fields in the radiative tachocline implies that there cannot be a slow tachocline; the dynamics should always be fast there, dominated by MHD. These results are obtained using solar parameters, but they should also apply generally to stars with convecting shells and perhaps also with convective cores.
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