Abstract
Let X be a locally finite tree, and let G = Aut(X). Then G is a locally compact group. We show that if X has more than one end, and if G contains a discrete subgroup Γ such that the quotient graph of groups Γ\\X is infinite but has finite covolume, then G contains a nonuniform lattice, that is, a discrete subgroup Λ such that Λ\G is not compact, yet has a finite G-invariant measure.