  We consider two dimensional conformal field theory (CFT) with large central
charge c in an excited state obtained by the insertion of an operator \Phi with
large dimension \Delta_\Phi ~ O(c) at spatial infinities in the thermal state.
We argue that correlation functions of light operators in such a state can be
viewed as thermal correlators with a rescaled effective temperature. The
effective temperature controls the growth of out-of-time order (OTO)
correlators and results in a violation of the universal upper bound on the
associated Lyapunov exponent when \Delta_\Phi <0 and the CFT is nonunitary. We
present a specific realization of this situation in the holographic
Chern-Simons formulation of a CFT with {W}^{(2)}_3 symmetry also known as the
Bershadsky-Polyakov algebra. We examine the precise correspondence between the
semiclassical (large-c) representations of this algebra and the Chern-Simons
formulation, and infer that the holographic CFT possesses a discretuum of
degenerate ground states with negative conformal dimension \Delta_\Phi =- c/8.
Using the Wilson line prescription to compute entanglement entropy and OTO
correlators in the holographic CFT undergoing a local quench, we find the
Lyapunov exponent \lambda_L = 4\pi/ \beta, violating the universal chaos bound.
