A precision measurement of the masses of the ${\mathrm{\ensuremath{\Lambda}}}^{0}$ and \ensuremath{\Lambda}${\mathrm{\ifmmode\bar\else\textasciimacron\fi{}}}^{0}$ hyperons is obtained from Gaussian fits to the invariant mass distributions for 20 138 ${\mathrm{\ensuremath{\Lambda}}}^{0}$'s and 18 309 \ensuremath{\Lambda}${\mathrm{\ifmmode\bar\else\textasciimacron\fi{}}}^{0}$'s. The Gaussians have standard deviations of 0.49 and 0.51 MeV/${\mathit{c}}^{2}$ for the ${\mathrm{\ensuremath{\Lambda}}}^{0}$ and \ensuremath{\Lambda}${\mathrm{\ifmmode\bar\else\textasciimacron\fi{}}}^{0}$, respectively. Systematic errors were reduced by calibrating the spectrometer with 60 000 exclusive events containing a ${\mathit{K}}_{\mathit{S}}^{0}$. We find ${\mathit{M}}_{\mathrm{\ensuremath{\Lambda}}}$=1115.678\ifmmode\pm\else\textpm\fi{}0.006\ifmmode\pm\else\textpm\fi{}0.006 MeV/${\mathit{c}}^{2}$ and ${\mathit{M}}_{\mathrm{\ensuremath{\Lambda}}\mathrm{\ifmmode\bar\else\textasciimacron\fi{}}}$=1115.690\ifmmode\pm\else\textpm\fi{}0.008\ifmmode\pm\else\textpm\fi{}0.006 MeV/${\mathit{c}}^{2}$. The ${\mathrm{\ensuremath{\Lambda}}}^{0\mathrm{\ensuremath{-}}}$\ensuremath{\Lambda}${\mathrm{\ifmmode\bar\else\textasciimacron\fi{}}}^{0}$ mass difference testing CPT invariance is -0.012\ifmmode\pm\else\textpm\fi{}0.010 MeV/${\mathit{c}}^{2}$.