We have performed a search for the eta_{b}(1S) meson in the radiative decay of the Upsilon(2S) resonance using a sample of 91.6x10(6) Upsilon(2S) events recorded with the BABAR detector at the PEP-II B factory at the SLAC National Accelerator Laboratory. We observe a peak in the photon energy spectrum at Egamma=609.3(-4.5)(+4.6)(stat)+/-1.9(syst) MeV, corresponding to an eta(b)(1S) mass of 9394.2(-4.9)(+4.8)(stat)+/-2.0(syst) MeV/c2. The branching fraction for the decay Upsilon(2S)-->gamma(eta)b(1S) is determined to be [3.9+/-1.1(stat)-0.9+1.1(syst)]x10(-4). We find the ratio of branching fractions B[Upsilon(2S)-->gamma(eta)b(1S)]/B[Upsilon(3S)-->gamma(eta)b(1S)]=0.82+/-0.24(stat)(-0.19)(+0.20)(syst).