THE rotation of the Sun is not that of a rigid body; at its surface, the gas near the poles has a lower angular velocity than that near the equator(1). This latitudinal variation persists to the base of the convection zone, below which the angular velocity becomes approximately uniform(2,3). Any variations of angular velocity at much greater depths are, however, poorly constrained(4-10). Observations of solar oscillation modes have been used to probe density variations in the Sun; rotational splitting of degenerate modes, although difficult to resolve, provides important constraints on the dynamical structure(11). Here we report observations of rotationally split : modes made over a three-year period with the Birmingham Solar Oscillations Network. Our results indicate that there is a substantial region inside the Sun that is rotating more slowly than the surface. This situation seems likely to be transient-the minimum-energy state would have all the deeper regions rotating with the same angular velocity-and is at variance with our current ideas about the rotational evolution of main-sequence stars(12). We have no solution to the dynamical problem this poses.