  The low-energy limit of string theory contains an anomaly-canceling
correction to the Einstein-Hilbert action, which defines an effective theory:
Chern-Simons (CS) modified gravity. The CS correction consists of the product
of a scalar field with the Pontryagin density, where the former can be treated
as a background field (non-dynamical formulation) or as an evolving field
(dynamical formulation). Many solutions of general relativity persist in the
modified theory; a notable exception is the Kerr metric, which has sparked a
search for rotating black hole solutions. Here, for the first time, we find a
solution describing a rotating black hole within the dynamical framework, and
in the small-coupling/slow-rotation limit. The solution is axisymmetric and
stationary, constituting a deformation of the Kerr metric with dipole scalar
"hair," whose effect on geodesic motion is to weaken the frame-dragging effect
and shift the location of the inner-most stable circular orbit outwards
(inwards) relative to Kerr for co-rotating (counter-rotating) geodesics. We
further show that the correction to the metric scales inversely with the fourth
power of the radial distance to the black hole, suggesting it will escape any
meaningful bounds from weak-field experiments. For example, using binary pulsar
data we can only place an initial bound on the magnitude of the dynamical
coupling constant of $\xi^{1/4} \lesssim 10^{4} {\textrm{km}}$. More stringent
bounds will require observations of inherently strong-field phenomena.
