  Activated Random Walk (ARW) is an interacting particle system on the
$d$-dimensional lattice $\mathbb{Z}^d$. On a finite subset $V \subset
\mathbb{Z}^d$ it defines a Markov chain on $\{0,1\}^V$. We prove that when $V$
is a Euclidean ball intersected with $\mathbb{Z}^d$, the mixing time of the ARW
Markov chain is at most $1+o(1)$ times the volume of the ball. The proof uses
an exact sampling algorithm for the stationary distribution, a coupling with
internal DLA, and an upper bound on the time when internal DLA fills the entire
ball. We conjecture cutoff at time $\zeta$ times the volume of the ball, where
$\zeta<1$ is the limiting density of the stationary state.
