  We present the first observation of the bottomonium ground state eta_b(1S) in
the photon energy spectrum using a sample of 109+/-1 million of Upsilon(3S)
events recorded at the Upsilon(3S) energy with the BaBar detector at the PEP-II
B factory at SLAC. A peak at E_gamma = 921.2 {+2.1}{-2.8}(stat) +/- 2.4(syst)
MeV observed with a significance of 10 standard deviations in the photon energy
spectrum is interpretated as being due to 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/c2. The hyperfine
Upsilon(1S)-eta_b(1S) mass splitting is 71.4 {+2.3}{-3.1}(stat) +/- 2.7(syst)
MeV/c2. The branching fraction for this radiative \Upsilon(3S) decay is
obtained as (4.8 +/- 0.5(stat) +/- 1.2 (syst)) x 10^(-4).
