  We argue that there is an obstruction to placing theories with 't Hooft
anomalies on manifolds with a boundary, unless the symmetry associated with the
anomaly can be represented as a non-invariance under an Abelian transformation.
For a two dimensional conformal field theory we further demonstrate that all
anomalies except the usual trace anomaly are incompatible on a manifold with a
boundary. Our findings extend a known result whereby, under mild assumptions,
Lagrangian theories with chiral matter cannot be canonically quantized.
