  We perform the stability analysis of the Schwarzschild black hole in $f(R)$
gravity with the parity-violating Chern-Simons (CS) term coupled to a dynamical
scalar field $\theta$. For this purpose, we transform the $f(R)$ gravity into
the scalar-tensor theory by introducing a scalaron $\phi$, providing the
dynamical Chern-Simons modified gravity with two scalars. The perturbation
equation for the scalar $\theta$ is coupled to the odd-parity metric
perturbation equation, providing a system of two coupled second order
equations, while the scalaron is coupled to the even-parity perturbation
equation. This implies that the CS coupling affects the Regge-Wheeler equation,
while $f(R)$ gravity does not affect the Zerilli equation. It turns out that
the Schwarzschild black hole is stable against the external perturbations if
the scalaron is free from the tachyon.
