Because of the nature of the one-electron states in a metal in a magnetic field, the possibility exists that the charge density of the ground state does not have the periodicity of the lattice. We present an elementary theory which suggests the possibility of a laminar arrangement of electron density with planes parallel to the magnetic field. We show that such a state is consistent with group theory. If observable at all, this state should experimentally be seen only at extremely low temperatures and strong magnetic fields. © 1970 The American Physical Society.