  Let $T$ be a tile in $\mathbb{Z}^n$, meaning a finite subset of
$\mathbb{Z}^n$. It may or may not tile $\mathbb{Z}^n$, in the sense of
$\mathbb{Z}^n$ having a partition into copies of $T$. However, we prove that
$T$ does tile $\mathbb{Z}^d$ for some $d$. This resolves a conjecture of
Chalcraft.
