  The two-channel Kondo impurity model realizes a local non-Fermi liquid state
with finite residual entropy. The competition between the two channels drives
the system to an impurity quantum critical point. We show that the
out-of-time-ordered (OTO) commutator for the impurity spin reveals markedly
distinct behaviour depending on the low energy impurity state. For the one
channel Kondo model with Fermi liquid ground state, the OTO commutator vanishes
for late times, indicating the absence of the butterfly effect. For the two
channel case, the impurity OTO commutator is completely temperature independent
and saturates quickly to its upper bound 1/4, and the butterfly effect is
maximally enhanced. These compare favourably to numerics on spin chain
representation of the Kondo model. Our results imply that a large late time
value of the OTO commutator does not necessarily diagnose quantum chaos.
