  I. M. Chiswell has asked whether every group that admits a free isometric
action (without inversions) on a $\Lambda$-tree is orderable. We give an
example of a multiple HNN extension $\Gamma$ which acts freely on a
$\mathbb{Z}^2$-tree but which has non-trivial generalised torsion elements. The
existence of such elements implies that $\Gamma$ is not orderable.
