  A gauge invariant quantum field theory with a spacetime dependent
Chern-Simons coefficient is studied. Using a constraint formalism together with
the Schwinger action principle it is shown that non-zero gradients in the
coefficient induce magnetic-moment corrections to the Hall current and
transform vortex singularities into non-local objects. The fundamental
commutator for the density fluctuations is obtained from the action principle
and the Hamiltonian of the Chern-Simons field is shown to vanish only under the
restricted class of variations which satisfy the gauge invariance constraint.
