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