We observed the bright unidentified TeV γ -ray source HESS J1616-508 with the X-ray Imaging Spectrometers onboard the Suzaku satellite. No X-ray counterpart was found to a limiting flux of 3.1 × 10-13 erg s-1 cm-2 in the 2–10 keV band, which is some 60-times below the γ -ray flux in the 1–10 TeV band. This object is bright in TeV γ -rays, but very dim in the X-ray band, and thus is one of the best examples in the Galaxy of a “dark particle accelerator." We also detected soft thermal emission with kT ∼ 0.3–0.6keV near the location of HESS J1616-508. This may be due to a dust-grain scattering halo from the nearby bright supernova remnant RCW 103.