Two-dimensional solids of particles with short-range attraction exhibit a solid-solid critical point. We report computer simulations that show that, near this point, the crystal becomes unstable to dislocation unbinding. Since the concentration of free dislocations is very small the resulting phase should be a stable hexatic phase. As the range of the attraction grows, the hexatic pocket expands and moves towards the melting curve. Such hexatic phases near a solid-solid critical point should be experimentally observable in confined colloidal suspensions.