Measurement of the Inclusive Charmless Semileptonic Branching Ratio of B Mesons and Determination of |V{sub ub}|

We report a measurement of the inclusive charmless semileptonic branching fraction of B mesons in a sample of 89 million B{bar B} events recorded with the BABAR detector at the {Upsilon}(4S) resonance. Events are selected by fully reconstructing the decay of one B meson and identifying a charged lepton from the decay of the other B meson. The number of signal events is extracted from the hadronic mass distribution and is used to determine the ratio of branching fractions {Beta}({bar B} {yields} X{sub u}l{bar {nu}})/{Beta}({bar B} {yields} Xl{bar {nu}}) = (2.06 {+-} 0.25(stat) {+-} 0.23(syst) {+-} 0.36(theo)) x 10{sup -2}. Using the measured branching fraction for inclusive semileptonic B decays, we find {Beta}({bar B} {yields} X{sub u}l{bar {nu}}) = (2.24 {+-} 0.27(stat) {+-} 0.26(syst) {+-} 0.39(theo)) x 10{sup -3} and derive the CKM matrix element |V{sub ub}| = (4.62 {+-} 0.28(stat) {+-} 0.27(syst) {+-} 0.48(theo)) x 10{sup -3}.