A study of chi(b) meson production at LHCb is performed on proton-proton collision data, corresponding to 3.0 fb(-1) of integrated luminosity collected at centre-of-mass energies root s = 7 and 8 TeV. The fraction of gamma(nS) mesons originating from chi(b) decays is measured as a function of the gamma transverse momentum in the rapidity range 2.0 < y(gamma) < 4.5. The radiative transition of the chi(b) (3P) meson to gamma(3S) is observed for the first time. The chi(b)1 (3P) mass is determined to be m chi(b1) (3P) = 10 511.3 +/- 1.7 +/- 2.5MeV/c(2), where the first uncertainty is statistical and the second is systematic.