  Let $\Lambda = \mathbb{Z}^n$ with lexicographic ordering. $\Lambda$ is a
totally ordered group. Let $X = \Lambda^+ * \Lambda^+$. Then $X$ is a
$\Lambda$-tree. Analogous to the construction of graph $C^*$-algebras, we form
a groupoid whose unit space is the space of ends of the tree. The $C^*$-algebra
of the $\Lambda$-tree is defined as the $C^*$-algebra of this groupoid. We
prove some properties of this $C^*$-algebra.
