  We study the effects of introducing purely gravitational Chern-Simons
Lagrangian terms in ordinary Einstein gravity on stationary rotating black hole
solutions and on the associated thermodynamical properties, in a generic number
of dimensions which support these terms (i.e. in D = 4k-1). We analyze the
conditions, namely the number of vanishing angular momenta, under which the
contributions of the Chern-Simons term to the equations of motion and the black
hole entropy vanish. The particular case of a 7-dimensional theory in which a
purely gravitational Chern-Simons term is added to the Einstein-Hilbert
Lagrangian in D=7 dimensions is investigated in some detail. As we have not
been able to find exact analytic solutions in nontrivial cases, we turn to
perturbation theory and calculate the first-order perturbative correction to
the Myers-Perry metric in the case where all angular momenta are equal. The
expansion parameter is a dimensionless combination linear in the Chern-Simons
coupling constant and the angular momentum. Corrections to horizon and
ergosurface properties, as well as black hole entropy and temperature, are
presented.
