<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>B<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>¯</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>mixing at the<i>Υ</i>(4<i>S</i>)

We have measured ${B}^{0}$B${\ifmmode\bar\else\textasciimacron\fi{}}^{0}$ mixing by observing like-sign dilepton events in \ensuremath{\Upsilon}(4S) decay. Assuming that the semileptonic branching fractions of the charged and neutral B mesons are equal and that the \ensuremath{\Upsilon}(4S) decays to ${B}^{+}$${B}^{\mathrm{\ensuremath{-}}}$ 55% of the time and to ${B}^{0}$B${\ifmmode\bar\else\textasciimacron\fi{}}^{0}$ 45% of the time, we measure the mixing parameter r to be 0.19\ifmmode\pm\else\textpm\fi{}0.06\ifmmode\pm\else\textpm\fi{}0.06, where the first error is statistical and the second is systematic.