We report on results of a dedicated search for the CP-violating decay ${\mathit{K}}_{\mathit{L}}$\ensuremath{\rightarrow}${\mathrm{\ensuremath{\pi}}}^{0}$${\mathit{e}}^{+}$${\mathit{e}}^{\mathrm{\ensuremath{-}}}$. We have found no evidence for this decay mode and obtain a 90%-confidence upper limit of 5.5\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}9}$ for its branching ratio.