  A simple probe of chaos and operator growth in many-body quantum systems is
the out of time ordered four point function. In a large class of local systems,
the effects of chaos in this correlator build up exponentially fast inside the
so called butterfly cone. It has been previously observed that the growth of
these effects is organized along rays and can be characterized by a velocity
dependent Lyapunov exponent, $\lambda({\bf v})$. We show that this exponent is
bounded inside the butterfly cone as $\lambda({\bf v})\leq 2\pi T(1-|{\bf
v}|/v_B)$, where $T$ is the temperature and $v_B$ is the butterfly speed. This
result generalizes the chaos bound of Maldacena, Shenker and Stanford. We study
$\lambda({\bf v})$ in some examples such as two dimensional SYK models and
holographic gauge theories, and observe that in these systems the bound gets
saturated at some critical velocity $v_*<v_B$. In this sense, boosting a system
enhances chaos. We discuss the connection to conformal Regge theory, where
$\lambda({\bf v})$ is related to the spin of the leading large $N$ Regge
trajectory, and controls the four point function in an interpolating regime
between the Regge and the light cone limit. Finally, we comment on the
generalization of the chaos bound to boosted and rotating ensembles and clarify
some recent results on this in the literature.
