Near-Earth asteroid (162173) 1999 JU3 (henceforth JU3) is a potentially hazardous asteroid and the target of the Japanese Aerospace Exploration Agency's Hayabusa-2 sample return mission. JU3 is also a backup target for two other sample return missions: NASA's OSIRIS-REx and the European Space Agency's Marco Polo-R. We use dynamical information to identify an inner-belt, low-inclination origin through the ν6 resonance, more specifically, the region with 2.15 AU < a < 2.5 AU and i < 8°. The geometric albedo of JU3 is 0.07 ± 0.01, and this inner-belt region contains four well-defined low-albedo asteroid families (Clarissa, Erigone, Polana, and Sulamitis), plus a recently identified background population of low-albedo asteroids outside these families. Only two of these five groups, the background and the Polana family, deliver JU3-sized asteroids to the ν6 resonance, and the background delivers significantly more JU3-sized asteroids. The available spectral evidence is also diagnostic; the visible and near-infrared spectra of JU3 indicate it is a C-type asteroid, which is compatible with members of the background, but not with the Polana family because it contains primarily B-type asteroids. Hence, this background population of low-albedo asteroids is the most likely source of JU3.