We report the first measurement of the branching fraction f(00) for Gamma(4S) --> B(0)B(0). The data sample consists of 81.7 fb(-1) collected at the Gamma(4S) resonance with the BABAR detector at the SLAC PEP-II asymmetric-energy e(+)e(-) storage ring. Using partial reconstruction of the decay B(0) --> D(*+) l(-)nu(l) in which only the charged lepton and the soft pion from the decay D(*+) --> D(0)pi(+) are reconstructed, we obtain f(00) = 0.487 +/- 0.010(stat) +/- 0.008(syst). Our result does not depend on the branching fractions of B(0) --> D(*+)l(-)nu(l) and D(*+) --> D(0)pi(+) decays, on the ratio of the charged and neutral B meson lifetimes, nor on the assumption of isospin symmetry.