  In this paper, we investigate the stability of Boltzmann equation with large
external potential in $\mathbb{T}^3$. For a class of initial data with large
oscillations in $L^\infty_{x,v}$ around the local Maxwellian, we prove the
existence of a global solution to the Boltzmann equation provided the initial
perturbation is suitably small in $L^2$-norm. The large time behavior of the
Boltzmann solution with exponential decay rate is also obtained. This seems to
be the first result on the perturbation theory of large-amplitude non-constant
equilibriums for large-amplitude initial data.
