The χb1(3P) and χb2(3P) states are observed through their (3S)γ 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 (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 χb(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 the ~(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.