  Pole-skipping is a recently discovered signature of many-body quantum chaos
in collective energy dynamics. It establishes a precise connection between
resummed, all-order hydrodynamics and the underlying microscopic chaos. In this
paper, we demonstrate the existence of pole-skipping in holographic conformal
field theories with higher-derivative gravity duals. In particular, we first
consider Einstein-Hilbert gravity deformed by curvature-squared ($R^2$)
corrections and then type IIB supergravity theory with the $\alpha'^3 R^4$
term, where $\alpha'$ is set by the length of the fundamental string. The
former case allows us to discuss the effects of leading-order $1/N_c$
corrections (with $N_c$ being the number of colours of the dual gauge group)
and phenomenological coupling constant dependence. In Einstein-Gauss-Bonnet
theory, pole-skipping turns out to be valid non-perturbatively in the
Gauss-Bonnet coupling. The $\alpha'^3 R^4$ deformation enables us to study
perturbative inverse 't Hooft coupling corrections ($\alpha'^3 \sim 1 /
\lambda^{3/2}$) in $SU(N_c)$, $\mathcal{N} = 4$ supersymmetric Yang-Mills
theory with infinite $N_c$. While the maximal Lyapunov exponent characterising
quantum chaos remains uncorrected, the butterfly velocity is shown to depend
both on $N_c$ and the coupling. Several implications of the relation between
hydrodynamics and chaos are discussed, including an intriguing similarity
between the dependence of the butterfly velocity and the ratio of shear
viscosity to entropy density on stringy corrections.
