We search for pair production of supersymmetric top quarks (t over1), followed by R-parity violating decay t over1-->taub with a branching ratio beta, using 322 pb(-1) of pp over collisions at sqrt s=1.96 TeV collected by the upgraded Collider Detector at Fermilab. Two candidate events pass our final selection criteria, consistent with the standard model expectation. We set upper limits on the cross section sigma(t over1t over1) x beta2 as a function of the top-squark mass m(t over1). Assuming beta=1, we set a 95% confidence level limit m(t over1)>153 GeV/c2. The limits are also applicable to the case of a third-generation scalar leptoquark (LQ3) decaying LQ3-->taub.