  Spinning black holes in dynamical Einstein-Chern-Simons gravity are
constructed by directly solving the field equations, without resorting to any
perturbative expansion. This model is obtained by adding to the
Einstein-Hilbert action a particular higher-curvature correction: the
Pontryagin density, linearly coupled to a scalar field. The spinning black
holes are stationary, axi-symmetric, asymptotically flat generalisations of the
Kerr solution of Einstein's gravity, but they possess a non-trivial
(odd-parity) scalar field. They are regular on and outside the horizon and
satisfy a generalized Smarr relation. We discuss the deviations from Kerr at
the level of the spin and mass distribution, the horizon angular velocity, the
ergo-region and some basic properties of geodesic motion. For sufficiently
small values of the Chern-Simons coupling our results match those previously
obtained using a perturbative approach.
