  We describe the effect of the gravitational $\Theta$-parameter on the
behavior of the stretched horizon of a black hole in $(3+1)$-dimensions. The
gravitational $\Theta$-term is a total derivative, however, it affects the
transport properties of the horizon. In particular, the horizon acquires a
third order parity violating, dimensionless transport coefficient which affects
the way localized perturbations scramble on the horizon. In the context of the
gauge/gravity duality, the $\Theta$-term induces a non-trivial contact term in
the energy-momentum tensor of a $(2+1)-$dimensional large-N gauge theory, which
admits a dual gravity description. As a consequence, the dual gauge theory in
the presence of the $\Theta$-term acquires the same third order parity
violating transport coefficient.
