  We compute the holographic entanglement entropy for the anomaly polynomial
$\mathrm{Tr} R^2$ in 3+1 dimensions. Using the perturbative method developed
for computing entanglement entropy for quantum field theories, we also compute
the parity odd contribution to the entanglement entropy of the dual field
theory that comes from a background gravitational Chern-Simons term. We find
that, in leading order in the perturbation of the background geometry, the two
contributions match except for a logarithmic divergent term on the field theory
side. We interpret this extra contribution as encoding our ignorance of the
source which creates the perturbation of the geometry.
