  We formulate the Chern-Simons action for any compact Lie group using Deligne
cohomology. This action is defined as a certain function on the space of smooth
maps from the underlying 3-manifold to the classifying space for principal
bundles. If the 3-manifold is closed, the action is a function with values in
complex numbers. If the 3-manifold is not closed, then the action is a section
of a Hermitian line bundle associated with the Riemann surface which appears as
the boundary.
