  The stability of the Maxwellian of the Boltzmann equation with a large
amplitude external potential $\Phi$ has been an important open problem. In this
paper, we resolve this problem with a large $C3-$potential in a periodic box
$\mathbb{T}^d$, $d \geq 3$. We use [1] in $L^p-L^{\infty}$ framework to
establish the well-posedness and the $L^{\infty}-$stability of the Maxwellian
$\mu_E(x,v)=\exp\{-\frac{|v|^2}{2}-\Phi(x)\}$.
