We present a search for pair produced top squarks, the supersymmetric partners of the top quark, using the D0 detector at the Fermilab Tevatron $p\overline{p}$ collider. We consider a scenario in which the lighter of the two top squarks ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{t}}_{1}$ decays with 100% branching fraction to a charm quark and the lightest neutralino ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\chi}}}_{1}^{0}$ yielding a signal of two acollinear jets with missing transverse energy. We observe 3 events while we expect $3.5\ifmmode\pm\else\textpm\fi{}1.2$ events from the known standard model processes. We exclude at the 95% confidence level a significant region of the ${m}_{{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{t}}_{1}}$- ${m}_{{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\chi}}}_{1}^{0}}$ parameter space. The highest ${m}_{{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{t}}_{1}}$ value we exclude is $93\mathrm{GeV}{/c}^{2}$ with a corresponding ${m}_{{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\chi}}}_{1}^{0}}$ value of $8\mathrm{G}\mathrm{e}\mathrm{V}/{c}^{2}$.