We observed the bright unidentified TeV gamma-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 3.1e-13 erg/s/cm^2 in the 2--10 keV band, which is some 60 times below the gamma-ray flux in the 1--10 TeV band. This object is bright in TeV gamma-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--0.6 keV near the location of HESSJ1616. This may be due to the dust grain scattering halo from the nearby bright supernova remnant RCW103.