  We report a new search for dark matter in a data sample of an integrated
luminosity of 7.7 fb$^{-1}$ of Tevatron $p\bar{p}$ collisions at $\sqrt{s} =
1.96$ TeV, collected by the CDF II detector. We search for production of a dark
matter candidate, $D$, in association with a single top quark. We consider the
hadronic decay mode of the top quark exclusively, yielding a final state of
three jets with missing transverse energy. The data are consistent with the
standard model; we thus set 95% confidence level upper limits on the cross
section of the process $p\bar{p}\rightarrow t+D$ as a function of the mass of
the dark-matter candidate. The limits are approximately 0.5 pb for a
dark-matter particle with mass in the range of 0-150 GeV/$c^{2}$.
