We have measured the cross section of the 7Be(p,gamma)8B reaction for E(c.m.) = 185.8, 134.7, and 111.7 keV using a radioactive 7Be target (132 mCi). Single and coincidence spectra of beta+ and alpha particles from 8B and 8Be* decay, respectively, were measured using a large acceptance spectrometer. The zero energy S factor inferred from these data is 18.5+/-2.4 eV b and a weighted mean value of 18.8+/-1.7 eV b (theoretical uncertainty included) is deduced when combining this value with our previous results at higher energies.