We present an assessment of the barium abundance ratios for red giant member stars in the faint Hercules dwarf spheroidal (dSph) galaxy. Our results are drawn from intermediate-resolution FLAMES/GIRAFFE spectra around the Ba II 6141.71 angstrom absorption line at low signal-to-noise ratios. For three brighter stars we were able to gain estimates from direct equivalent-width measurements, while for the remaining eight stars only upper limits could be obtained. These results are investigated in a statistical manner and indicate very low Ba abundances of log epsilon(Ba) less than or similar to 0.7 dex (3 sigma). We discuss various possible systematic biasses, first and foremost, a blend with the Fe I 6141.73 angstrom-line, but most of those would only lead to even lower abundances. A better match with metal-poor halo and dSph stars can only be reached by including a large uncertainty in the continuum placement. This contrasts with the high dispersions in iron and calcium (in excess of 1 dex) in this galaxy. While the latter spreads are typical of the very low luminosity, dark-matter dominated dSphs, a high level of depletion in heavy elements suggests that chemical enrichment in Hercules was governed by very massive stars, coupled with a very low star formation efficiency. While very low abundances of some heavy elements are also found in individual stars of other dwarf galaxies, this is the first time that a very low Ba abundance is found within an entire dSph over a broad metallicity range.