  Celestial holography proposes a duality between gravitational scattering in
asymptotically flat space-time and a conformal field theory living on the
celestial sphere. Its dictionary relates the infinite dimensional space-time
symmetry group to Ward identities of the CFT. The spontaneous breaking of these
asymptotic symmetries governs the dynamics of the soft sector in the CFT. Here
we show that this sector encodes non-trivial backreaction effects that exhibit
characteristics of maximal quantum chaos. A key element in the derivation is
the identification of the Hilbert space of celestial CFT, defined through
radial quantization, with that of a constantly accelerating Rindler observer.
From the point of view of the bulk, Rindler particles exhibit Lyapunov behavior
due to shockwave interactions that shift the observer horizon. From the point
of view of the boundary, the superrotation Goldstone modes affect the relevant
representations of the celestial Virasoro symmetry in a manner that induces
Lyapunov behavior of out-of-time-ordered celestial correlators.
