Abstract: We report a measurement of the branching fraction of the exclusive charmless semileptonic decay B+ -> omega l(+) nu, where l is either an electron or amuon. We use samples of B+ mesons tagged by a reconstructed charmed semileptonic decay of the other B meson in the event. The measurement is based on a data set of 426.1 fb(-1) of e(+)e(-) collisions at a center-of-mass energy of 10.58 GeV recorded with the BABAR detector at the PEP-II asymmetric-energy e(+)e(-) storage rings. We measure a branching fraction of B(B+ -> omega l(+) nu) = (1.35 +/- 0.21 +/- 0.11) x 10(-4), where the uncertainties are statistical and systematic, respectively. We also present measurements of the partial branching fractions in three bins of q(2), the invariant-mass squared of the lepton-neutrino system, and we compare them to theoretical predictions of the form factors.