The $B^0$-$bar B^0$ oscillation frequency has been measured with a sample of 23 million $Bbar B$ pairs collected with the BABAR detector at the PEP-II asymmetric B Factory at SLAC. In this sample, we select events in which both B mesons decay semileptonically and use the charge of the leptons to identify the flavor of each B meson. A simultaneous fit to the decay time difference distributions for opposite- and same-sign dilepton events gives $Delta m_d = 0.493 pm 0.012{(stat)}pm 0.009{(syst)}$ ps$^{-1}$.