  In this paper we investigate measures of chaos and entanglement in rational
conformal field theories in 1+1 dimensions. First, we derive a universal
formula for the late time value of the out-of-time-ordered correlators for this
class of theories. Our universal result can be expressed as a particular
combination of the modular S-matrix elements known as the anyon monodromy
scalar. Next, in the explicit setup of a $SU(N)_k$ Wess-Zumino-Witten model, we
compare the late time behavior of the out-of-time-ordered correlators and the
purity. Interestingly, in the large-c limit, the purity grows logarithmically
as in holographic theories; in contrast, the out-of-time-ordered correlators
remain, in general, non-vanishing.
