  We study out-of-time-order correlators (OTOCs) of rotating BTZ black holes
using two different approaches: the elastic eikonal gravity approximation, and
the Chern-Simons formulations of 3-dimensional gravity. Within both methods the
OTOC is given as a sum of two contributions, corresponding to left and right
moving modes. The contributions have different Lyapunov exponents,
$\lambda_L^{\pm}=\frac{2\pi}{\beta}\frac{1}{1\mp \ell \Omega}$, where $\Omega$
is the angular velocity and $\ell$ is the AdS radius. Since $\lambda_L^{-} \leq
\frac{2\pi}{\beta} \leq \lambda_L^{+}$, there is an apparent contradiction with
the chaos bound. We discuss how the result can be made consistent with the
chaos bound if one views $\beta_{\pm}=\beta(1\mp \ell \Omega)$ as the effective
inverse temperatures of the left and right moving modes.
