We report the observation of gamma(2S) -> gamma eta(b)(1S) based on an analysis of the inclusive photon spectrum of 24.7 fb(-1) of e(+)e(-) collisions at the gamma(2s) center-of-mass energy collected with the Belle detector at the KEKB asymmetric-energy e(+)e(-) collider. We measure a branching fraction of B [gamma(2S) -> gamma eta(b)(1S)] = (6.1(-0.7-0.6)(+0.6+0.9) x 10(-4) and derive an eta(b) (1S) mass of 9394.8(-3.1-2.7)(+2.7+4.5) MeV/c(2), where the uncertainties are statistical and systematic, respectively. The significance of our measurement is greater than 7 standard deviations, constituting the first observation of this decay mode.