Many models of physics beyond the standard model predict the existence of new Abelian forces with new gauge bosons mediating interactions between "dark sectors" and the standard model. We report a search for a dark boson Z ′ coupling only to the second and third generations of leptons in the reaction e + e − → μ + μ − Z ′ , Z ′ → μ + μ − using 514     fb − 1 of data collected by the BABAR experiment. No significant signal is observed for Z ′ masses in the range 0.212-10 GeV. Limits on the coupling parameter g ′ as low as 7 × 10 − 4 are derived, leading to improvements in the bounds compared to those previously derived from neutrino experiments.