  We explore the quantum chaos of the coadjoint orbit action. We study quantum
fluctuation around a saddle point to evaluate the soft mode contribution to the
out-of-time-ordered correlator. We show that the stability condition of the
semi-classical analysis of the coadjoint orbit found by Witten (1988) leads to
the upper bound on the Lyapunov exponent which is identical to the bound on
chaos proven in arXiv:1503.01409. The bound is saturated by the coadjoint orbit
$\text{Diff}(S^1)/SL(2)$ while the other stable orbit $\text{Diff}(S^1)/U(1)$
where the $SL(2,\mathbb{R})$ is broken to $U(1)$ has non-maximal Lyapunov
exponent.
