  We find an effective action for gravitational interactions with scalars in
$AdS_3$ to first order in $G_N$ at the conformal boundary. This action can be
understood as an action for the Brown-Henneaux modes and is given by the
square-root product of right and left moving Schwarzian derivatives for
conformal transformations of the boundary. We thus reproduce the result
$\lambda_L=\frac{2\pi}{\beta}$ for OTOC computed first in arXiv:1412.6087 for a
Schwarzchild black hole in $AdS_3$. Applying the same procedure to rotating BTZ
we find the Lyapunov index to be
$\lambda_L=\frac{2\pi}{\beta_+}>\frac{2\pi}{\beta}$ where
$\beta_+=\beta(1-\mu_L)$, with $\mu_L=\frac{r_-}{r_+}$ being the chemical
potential for angular momentum. We thus comment on a possible modification to a
part of the proof given in arXiv:1503.01409 to accommodate this result.
