  G\"{o}del-type metrics that are homogeneous in both space and time remain,
like the Schwarzschild metric, consistent within Chern-Simons modified gravity;
this is true in both the non-dynamical and dynamical frameworks, each of which
involves an additional pseudoscalar field coupled to the Pontryagin density. In
this paper, we consider static, first-order perturbations to these metrics in
the non-dynamical framework. Under certain assumptions we find analytical
solutions to the perturbed field equations. The solutions of the first-order
field equations break the translational and cylindrical symmetries of the
unperturbed metrics. The effective potential controlling planar geodesic orbits
is also affected by the perturbation parameter, which changes the equilibrium
radii for the orbits of both massive particles and massless photons.
