  We derive the framing anomaly of four-dimensional holomorphic-topological
Chern-Simons theory formulated on the product of a topological surface and the
complex plane. We show that the presence of this anomaly allows one to couple
four-dimensional Chern-Simons theory to holomorphic field theories with
Kac-Moody symmetry, where the Kac-Moody level $k$ is critical $k=-h^{\vee}$.
Applying this result to a holomorphic sigma model into a complex coadjoint
orbit, we derive that four-dimensional Chern-Simons theory admits holomorphic
monodromy defects.
