  We derive macroscopic expressions for the polarization and orbital
magnetization of a Chern insulator in its zero-temperature ground state using a
previously developed formalism for treating microscopic polarization and
magnetization fields in extended media. In the limit of a topologically trivial
insulator, our results reduce to those of the "modern theories of polarization
and magnetization." In a Chern insulator, however, we find a generically
nonvanishing microscopic free current density, the macroscopic average of which
vanishes. Moreover, the expression that we obtain for the polarization is
qualitatively similar to that of the "modern theory," while the expressions for
the orbital magnetization fundamentally differ; the manner in which they differ
elucidates the distinct philosophies of these theoretical frameworks.
