The mass of the eta(b)(1S), measured recently by the BABAR Collaboration, is significantly lower than expected from QCD predictions for the Upsilon(1S)-eta(b)(1S) hyperfine splitting. We suggest that the observed eta(b)(1S) mass is shifted downwards due to a mixing with a CP-odd Higgs boson A with a mass m(A) in the range 9.4-10.5 GeV compatible with LEP, CLEO, and BABAR constraints. We determine the resulting predictions for the spectrum of the eta(b)(nS)-A system and the branching ratios into tau(+)tau(-) as functions of m(A).