A region with an appreciable hydrogen gradient arises beneath the base of the convection zone during the evolution of the Sun. This region formes due to the interaction between diffusive chemical segregation and evolutionary motion of the boundary of convective mixing, that is, changes in the mass of the convection zone. A physical model for the evolution of this chemical-composition gradient is proposed, based on a numerical solution of the drift-diffusion equation with discontinuous coefficients, using post-model computations of the evolution of the chemical composition. This model is used to investigate possible traces of the early evolution in the hydrogen profile in the present Sun. Data on this profile can be obtained using helioseimic inversion of the buoyancy frequency in this region. Analysis indicates the presence of an enhanced hydrogen gradient in the region of the tachocline, which could be explained by either additional weak mixing or a greater depth of the solar convection zone when the Sun was on the Zero-Age Main Sequence.