  We derive an initial value formulation for dynamical Chern-Simons gravity, a
modification of general relativity involving parity-violating higher derivative
terms. We investigate the structure of the resulting system of partial
differential equations thinking about linearization around arbitrary
backgrounds. This type of consideration is necessary if we are to establish
well-posedness of the Cauchy problem. Treating the field equations as an
effective field theory we find that weak necessary conditions for hyperbolicity
are satisfied. For the full field equations we find that there are states from
which subsequent evolution is not determined. Generically the evolution system
closes, but the full field equations are in no sense hyperbolic. In a cursory
mode analysis we find that the equations of motion contain terms that may cause
ill-posedness of the initial value problem.
