  We study scalarization of slowly rotating black holes in the
Einstein-scalar-Gauss-Bonnet (GB)-Chern-Simons (CS) theory. In the slow
rotation approximation of $a\ll1$ with rotation parameter $a$, the GB term is
given by a term for Schwarzschild black hole, whereas the CS term takes a
linear term of $a$. The tachyonic instability for slowly rotating black holes
represents the onset of spontaneous scalarization. We use the (2+1)-dimensional
hyperboloidal foliation method to show the tachyonic instability for slowly
rotating black holes by considering the time evolution of a spherically
symmetric scalar mode. A threshold (existence) curve is obtained from the
constant scalar modes under time evolution, which means the boundary between
stable and unstable black holes. It is found that the slowly rotating black
holes turn out to be unstable against a spherically symmetric scalar-mode
propagation for positive coupling $\alpha$. However, we could not find
tachyonic instability and any $a$-bound for scalarization for negative coupling
$\alpha$.
