The entropic depletion force in colloids arises when large particles are placed in a solution of smaller ones and sterically constrained to avoid them. We calculate the interaction between two hard spheres (of radius R) in a semidilute solution of hard rods of length L and diameter D (D << L << R) to second order in rod concentration. In addition to the well-known attractive force for separations less than L, we find a repulsive force between the spheres at larger separations. For semidilute rods, the resulting barrier can be large compared to k(B)T, permitting kinetic stabilization.