Let Λ = Zⁿ with lexicographic ordering. Λ is a totally ordered group. Let X = Λ⁺ * Λ⁺. Then X is a Λ-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 Λ-tree is defined as the C*-algebra of this groupoid. We prove some properties of this C*-algebra.