  We study the effective action for strong-coupling lattice QCD with
one-component staggered fermions in the case of nonzero chemical potential and
zero temperature. The structure of this action suggests that at large chemical
potentials its ground state is a crystalline `chiral density wave' that
spontaneously breaks chiral symmetry and translation invariance. In mean-field
theory, on the other hand, we find that this state is unstable. We show that
lattice artifacts are partly responsible for this, and suggest that if this
phase exists in QCD, then finding it in Monte-Carlo simulations would require
simulating on relatively fine lattices. In particular, the baryon mass in
lattice units, m_B, should be considerably smaller than its strong-coupling
limit of m_B~3.
