  We report the first measurement of the branching fraction f00 for Upsilon(4S)
--> B0B0bar. The data sample consists of 81.7 fb^-1 collected at the
Upsilon(4S) resonance with the BABAR detector at the PEP-II asymmetric-energy
e^+e^- storage ring. Using partial reconstruction of the decay B0bar --> D^{*+}
\ell^{-} \bar{\nu}_{\ell} in which only the charged lepton and the soft pion
from the decay D^{*+} --> D0 pi^+ are reconstructed, we obtain f00 = 0.487 \pm
0.010(stat) \pm 0.008(sys). Our result does not depend on the branching
fractions of B0bar --> D^{*+} \ell^{-} \bar{\nu}_{\ell} and D^{*+} --> D0 pi^+
decays, on the ratio of the charged and neutral B meson lifetimes, nor on the
assumption of isospin symmetry.
