  We extend the Berry-phase concept of polarization to insulators having a
non-zero value of the Chern invariant. The generalization to such Chern
insulators requires special care because of the partial occupation of chiral
edge states. We show how the integrated bulk current arising from an adiabatic
evolution can be related to a difference of bulk polarizations. We also show
how the surface charge can be related to the bulk polarization, but only with a
knowledge of the wavevector at which the occupancy of the edge state is
discontinuous. Furthermore we present numerical calculations on a model
Hamiltonian to provide additional support for our analytic arguments.
