We present measurements of the time-dependent $CP$-violating asymmetries in ${B}^{0}\ensuremath{\rightarrow}{K}_{S}^{0}{K}_{S}^{0}{K}_{S}^{0}$ decays based on $384\ifmmode\times\else\texttimes\fi{}{10}^{6}$ $\ensuremath{\Upsilon}(4S)\ensuremath{\rightarrow}B\overline{B}$ decays collected with the BABAR detector at the PEP-II asymmetric-energy $B$ Factory at SLAC. We obtain the $CP$ asymmetry parameters $C=0.02\ifmmode\pm\else\textpm\fi{}0.21\ifmmode\pm\else\textpm\fi{}0.05$ and $S=\ensuremath{-}0.71\ifmmode\pm\else\textpm\fi{}0.24\ifmmode\pm\else\textpm\fi{}0.04$, where the first uncertainties are statistical and the second systematic. These results are consistent with standard model expectations.
