We report the results of a search for the bottomonium ground state
eta_b(1S) in the photon energy spectrum with a sample of (109 +/- 1)
million of Upsilon(3S) recorded at the Upsilon(3S) energy with the
BABAR detector at the PEP-II B factory at SLAC.  We observe a peak in
the photon energy spectrum at E_gamma = 921.2 +2.1 -2.8 (stat) +/-
2.4(syst) MeV with a significance of 10 standard deviations. We
interpret the observed peak as being due to monochromatic photons from
the radiative transition Upsilon(3S) -> gamma eta_b(1S).  This photon
energy corresponds to an eta_b(1S) mass of 9388.9 +3.1 -2.3 (stat)
+/- 2.7(syst) MeV/c^2.  The hyperfine Upsilon(1S)-eta_b(1S) mass
splitting is 71.4 +2.3 -3.1 (stat) +/- 2.7(syst) MeV/c^2.  The
branching fraction for this radiative Upsilon(3S) decay is estimated
to be (4.8 +/- 0.5(stat) +/- 1.2 (syst)) x 10^(-4).