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(\mathbbZ,G)X(\mathbb{Z},\Gamma) be the space of representations of \mathbbZ\mathbb{Z} into Γ modulo conjugation by Γ. X(\mathbbZ,G)X(\mathbb{Z},G) is defined similarly. Let p: X(\mathbbZ,G)® X(\mathbbZ,G)\pi : X(\mathbb{Z},\Gamma)\to X(\mathbb{Z},G) be the projection map. The PGT provides a volume form vol on X(\mathbbZ,G)X(\mathbb{Z},G) such that for sequences of subsets {B _t }, B_t Ì X(\mathbbZ,G)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 \mathbbZ\mathbb{Z} is replaced by a free group of finite rank under the additional hypothesis that n = 2 or 3.