We present the radial velocity curve of a single-lined spectroscopic binary in the faint Hercules dwarf spheroidal (dSph) galaxy, based on 34 individual spectra covering more than 2 yr of observations. This is the first time that orbital elements could be derived for a binary in a dSph. The system consists of a metal-poor red giant and a low-mass companion, possibly a white dwarf, with a 135 day period in a moderately eccentric (e = 0.18) orbit. Its period and eccentricity are fully consistent with metal-poor binaries in the Galactic halo, while the projected semimajor axis is small, at ap sin i = 38 R ☉. In fact, a very close orbit could inhibit the production of heavier elements through s-process nucleosynthesis, leading to the very low abundances of neutron-capture elements that are found in this star. We discuss the further implications for the chemical enrichment history of the Hercules dSph, but find no compelling binary scenario that could reasonably explain the full, peculiar abundance pattern of the Hercules dSph galaxy.