  Thermal states of quantum systems with many degrees of freedom are subject to
a bound on the rate of onset of chaos, including a bound on the Lyapunov
exponent, $\lambda_L\leq 2\pi /\beta$. We harness this bound to constrain the
space of putative holographic CFTs and their would-be dual theories of AdS
gravity. First, by studying out-of-time-order four-point functions, we discuss
how $\lambda_L=2\pi/\beta$ in ordinary two-dimensional holographic CFTs is
related to properties of the OPE at strong coupling. We then rule out the
existence of unitary, sparse two-dimensional CFTs with large central charge and
a set of higher spin currents of bounded spin; this implies the inconsistency
of weakly coupled AdS$_3$ higher spin gravities without infinite towers of
gauge fields, such as the $SL(N)$ theories. This fits naturally with the
structure of higher-dimensional gravity, where finite towers of higher spin
fields lead to acausality. On the other hand, unitary CFTs with classical
$W_{\infty}[\lambda]$ symmetry, dual to 3D Vasiliev or hs[$\lambda$] higher
spin gravities, do not violate the chaos bound, instead exhibiting no chaos:
$\lambda_L=0$. Independently, we show that such theories violate unitarity for
$|\lambda|>2$. These results encourage a tensionless string theory
interpretation of the 3D Vasiliev theory. We also perform some CFT calculations
of chaos in Rindler space in various dimensions.
