  We present a search for a new particle T' decaying to a top quark via T' -> t
+ X, where X goes undetected. We use a data sample corresponding to 5.7 fb-1 of
integrated luminosity of ppbar collisions with sqrt{s} = 1.96 TeV, collected at
Fermilab by the CDF II detector. Our search for pair production of T' is
focused on the hadronic decay channel, ppbar -> T'T' -> tt +XX -> bbqqqq + XX.
We interpret our results in terms of a model where T' is an exotic fourth
generation quark and X is a dark matter candidate. The data are consistent with
standard model expectations. We set a limit on the generic production of
T'T'->tt+XX, excluding the fourth generation exotic quarks T' at 95% confidence
level up to m_T' = 400 GeV/c2 for m_X < 70 GeV/c2.
