  Let $G \leq \mathrm{Sym} (X)$ for a countable set $X$. Call a colouring of
$X$ asymmetric, if the identity is the only element of $G$ which preserves all
colours. The motion (also called minimal degree) of $G$ is the minimal number
of elements moved by an element $g \in G \setminus\{\mathrm{id}\}$. We show
that every locally compact, closed permutation group with infinite motion
admits an asymmetric $2$-colouring. This generalises a recent result by Babai
and confirms a conjecture by Imrich, Smith, Tucker, and Watkins from 2015.
