  We present the results of a search for pair production of the supersymmetric
partner of the top quark (the stop quark $\tilde{t}_{1}$) decaying to a
$b$-quark and a chargino $\chargino$ with a subsequent $\chargino$ decay into a
neutralino $\neutralino$, lepton $\ell$, and neutrino $\nu$. Using a data
sample corresponding to 2.7 fb$^{-1}$ of integrated luminosity of $p\bar{p}$
collisions at $\sqrt{s} = 1.96$ TeV collected by the CDF II detector, we
reconstruct the mass of candidate stop events and fit the observed mass
spectrum to a combination of standard model processes and stop quark signal. We
find no evidence for $\pairstop$ production and set 95% C.L. limits on the
masses of the stop quark and the neutralino for several values of the chargino
mass and the branching ratio ${\cal B}(\chargino\to\neutralino\ell^{\pm}\nu)$.
