We report the results from an experimental search for strongly interacting massive particles bound to gold nuclei. A scan for heavy gold isotopes with masses ranging from 186.3 to $325.9 \mathrm{GeV}{/c}^{2}$ was performed on laboratory gold and gold from western Australia using PRIME Lab, the Purdue Accelerator Mass Spectrometer facility. The results provide significant new constraints on current models which predict the existence of such particles with abundance ratios in the range ${10}^{\ensuremath{-}11}\char21{}{10}^{\ensuremath{-}10}.$