A tree-free group that is not orderable

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