We report a new search for dark matter in a data sample of an integrated luminosity of 7.7 fb-1 of Tevatron pp[over ¯] collisions at √[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 pp[over ¯]→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/c2.