The chi(b1)(3P) and chi(b2)(3P) states are observed through their gamma(3S)(gamma) decays, using an event sample of proton-proton collisions collected by the CMS experiment at the CERN LHC. The data were collected at a center-of-mass energy of 13 TeV and correspond to an integrated luminosity of 80.0 fb(-1). The gamma(3S) mesons are identified through their dimuon decay channel, while the low-energy photons are detected after converting to e(+)e(-) pairs in the silicon tracker, leading to a chi(b)(3P) mass resolution of 2.2 MeV. This is the first time that the J = 1 and 2 states are well resolved and their masses individually measured: 10513.42 +/- 0.41(stat) +/- 0.18(syst) MeV and 10524.02 +/- 0.57(stat) +/- 0.18(syst) MeV; they are determined with respect to the world-average value of gamma(3S) mass, which has an uncertainty of 0.5 MeV. The mass splitting is measured to be 10.60 +/- 0.64(stat) +/- 0.17(syst) MeV.