The low surface rotation rate of the Sun and other main-sequence stars is believed to be the result of angular momentum loss due to a stellar wind1. This loss also leads to a differential rotation, the interior spinning more rapidly than the surface. The rate of increase with depth of the rotation speed is limited by hydrodynamic instabilities, which cause an outward diffusion of angular momentum2. The conditions for the occurrence of hydrodynamic instabilities in a radiative stellar interior are reviewed here assuming that the rotation is constant on spheres. The instability with the lowest threshold is a double diffusive one, the axisymmetric baroclinic diffusive (ABCD) instability. A minimum rotation curve for the present Sun is calculated using the assumption that the efficiency of this instability is sufficiently high that the rotation of the Sun is close to marginal stability. This lower limit to the internal rotation rate is roughly consistent with present observations of the rotational splitting of solar oscillations.