  We present a scheme for generating first-order metric perturbation initial
data for an arbitrary background and source. We then apply this scheme to
derive metric perturbations in order-reduced dynamical Chern-Simons gravity
(dCS). In particular, we solve for metric perturbations on a black hole
background that are sourced by a first-order dCS scalar field. This gives us
the leading-order metric perturbation to the spacetime in dCS gravity. We then
use these solutions to compute black hole shadows in the linearly perturbed
spacetime by evolving null geodesics. We present a novel scheme to decompose
the shape of the shadow into multipoles parametrized by the spin of the
background black hole and the perturbation parameter $\varepsilon^2$. We find
that we can differentiate the presence of a pure Kerr spacetime from a
spacetime with a dCS perturbation using the shadow, allowing in part for a
null-hypothesis test of general relativity. We then consider these results in
the context of the Event Horizon Telescope.
