  We analyze a holographic model with a pure gauge and a mixed
gauge-gravitational Chern-Simons term in the action. These are the holographic
implementations of the usual chiral and the mixed gauge-gravitational anomalies
in four dimensional field theories with chiral fermions. We discuss the
holographic renormalization and show that the gauge-gravitational Chern-Simons
term does not induce new divergences. In order to cancel contributions from the
extrinsic curvature at a boundary at finite distance a new type of counterterm
has to be added however. This counterterm can also serve to make the Dirichlet
problem well defined in case the gauge field strength vanishes on the boundary.
A charged asymptotically AdS black hole is a solution to the theory and as an
application we compute the chiral magnetic and chiral vortical conductivities
via Kubo formulas. We find that the characteristic term proportional to T^2 is
present also at strong coupling and that its numerical value is not
renormalized compared to the weak coupling result.
