We explore the connection between Mott-insulating behavior and the breakdown of lattice-translation symmetry. We find that if a system of hard-core particles in d=2 is given to be a Mott insulator, then the charge must form a commensurate charge-density wave. This is true for particles of any statistics. Our result is based on duality arguments and does not seem to depend on the details of the Hamiltonian. For average site-occupation number n<1, this implies a breakdown of lattice-translation symmetry. © 1990 The American Physical Society.