We study the effective Hamiltonian for strong-coupling lattice QCD in the case of a nonzero baryon density. In leading order the effective Hamiltonian is a generalized antiferromagnet. For naive fermions, the symmetry is U(4N f) and the spins belong to a representation that depends on the local baryon number. Next-nearest-neighbor (NNN) terms in the Hamiltonian break the symmetry to U(Nf) × U(Nf). We transform the quantum problem to a Euclidean sigma model which we analyze in a 1/Nc expansion. In the vacuum sector we recover spontaneous breaking of chiral symmetry for the nearest-neighbor and NNN theories. For a nonzero baryon density we study the nearest-neighbor theory only, and show that the pattern of spontaneous symmetry breaking depends on the baryon density.