The classical prime geodesic theorem (PGT) gives an asymptotic formula (as x tends to infinity) for the number of closed geodesics with length at most x on a hyperbolic manifold M. Closed geodesics correspond to conjugacy classes of π1(M) = Γ where Γ is a lattice in G = SO(n,1). The theorem can be rephrased in the following format. Let $$X(\mathbb{Z},\Gamma)$$ be the space of representations of $$\mathbb{Z}$$ into Γ modulo conjugation by Γ. $$X(\mathbb{Z},G)$$ is defined similarly. Let $$\pi : X(\mathbb{Z},\Gamma)\to X(\mathbb{Z},G)$$ be the projection map. The PGT provides a volume form vol on $$X(\mathbb{Z},G)$$ such that for sequences of subsets {B t }, $$B_t \subset X(\mathbb{Z},G)$$ satisfying certain explicit hypotheses, |π−1(B t )| is asymptotic to vol(B t ). We prove a statement having a similar format in which $$\mathbb{Z}$$ is replaced by a free group of finite rank under the additional hypothesis that n = 2 or 3.