  Dynamical Chern-Simons (DCS) theory is an extension of General Relativity in
which the gravitational field is coupled to a scalar field through a parity
violating term. We study perturbations of anti-de Sitter black holes and branes
in such a theory, and show that the relevant equations reduce to a set of
coupled ODEs which can be solved efficiently through a series expansion. We
prove numerically that black holes and branes in DCS gravity are stable against
gravitational and scalar perturbations in the entire parameter space.
Furthermore, by applying the AdS/CFT duality, we relate black hole
perturbations to hydrodynamic quantities in the dual field theory, which is a
(2+1)-dimensional isotropic fluid with broken spatial parity. The Chern-Simons
term does not affect the entropy to viscosity ratio and the relaxation time,
but instead quantities that enter the shear mode at order q^4 in the small
momentum limit, for example the Hall viscosity and other quantities related to
second and third order hydrodynamics. We provide explicit corrections to the
gravitational hydrodynamic mode to first relevant order in the couplings.
