We present a study of the decays B;{0,+}-->J/psiomegaK;{0,+} using 383x10;{6} BB[over ] events obtained with the BABAR detector at PEP-II. We observe Y(3940)-->J/psiomega, with mass 3914.6_{-3.4};{+3.8}(stat)+/-2.0(syst) MeV/c;{2}, and width 34_{-8};{+12}(stat)+/-5(syst) MeV. The ratio of B0 and B+ decay to YK is 0.27_{-0.23};{+0.28}(stat)-0.01+0.04(syst), and the relevant B0 and B+ branching fractions are reported.