  We perform a canonical and BRST analysis of a seven-dimensional Chern-Simons
theory on a manifold with boundary. The main result is that the 7D theory
induces for consistency a chiral two-form on the 6D boundary. We also comment
on similar behaviour in a five-dimensional Chern-Simons theory relevant for
$\N=4$ supersymmetric Yang-Mills theory in four dimensions.
