  We discuss a Chern-Simons (CS) scalar field around a rapidly rotating black
hole in dynamical CS modified gravity. The CS correction can be obtained
perturbatively by considering the Kerr spacetime to be the background. We
obtain the CS scalar field solution around the black hole analytically and
numerically, assuming a stationary and axisymmetric configuration. The scalar
field diverges on the inner horizon when we impose the boundary condition that
the scalar field is regular on the outer horizon and vanishes at infinity.
Therefore, the CS scalar field becomes problematic on the inner horizon.
