We have studied in some detail the possibility of observing CP violation in the B-meson system using asymmetric-energy ${e}^{+}$${e}^{\mathrm{\ensuremath{-}}}$ beams colliding with a center-of-mass energy corresponding to the \ensuremath{\Upsilon}(4S) mass. If a CP eigenstate is detected in conjunction with an identified ${B}^{0}$ or B${\ifmmode\bar\else\textasciimacron\fi{}}^{0}$, the distribution of the flight path between decays contains a term which provides a measurement of CP violation, as discussed in this paper. The moving B mesons in the laboratory make this flight-path measurement possible. The use of the \ensuremath{\Upsilon}(4S) provides the largest BB\ifmmode\bar\else\textasciimacron\fi{} cross section in ${e}^{+}$${e}^{\mathrm{\ensuremath{-}}}$ production, other than from the ${Z}^{0}$, and allows excellent background rejection because the B is monoenergetic in the center-of-mass frame. Since there are no extra fragmentation products accompanying the BB\ifmmode\bar\else\textasciimacron\fi{} in the event, very simple tagging strategies can be used to separate ${B}^{0}$ from B${\ifmmode\bar\else\textasciimacron\fi{}}^{0}$ decays, providing a tagging efficiency close to 50%. The CP eigenstates studied in this paper are J/\ensuremath{\psi}+${K}_{S}^{0}$, J/\ensuremath{\psi}+${K}^{\mathrm{*}0}$ and \ensuremath{\psi}'+${K}_{S}^{0}$. Given an adequate detector, the integrated luminosity needed to observe CP violation in the standard model is expected to be about 2\ifmmode\times\else\texttimes\fi{}${10}^{40}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}2}$ or ${10}^{7}$ produced ${B}^{0}$B${\ifmmode\bar\else\textasciimacron\fi{}}^{0}$ pairs.