Abstract: The neutron capture cross sections of (186)Os and (187)Os are of key importance for defining the 8-process abundance of (187)Os at the formation of the solar system. This quantity can be used to determine the radiogenic abundance component of (187)Os from the decay of (187)Re (t(1/2) = 41.2 Gyr) and to infer the time-duration of the nucleosynthesis in our galaxy (Re/Os cosmochronometer). The neutron capture cross sections of (186)Os, (187)Os, and (188)Os have been measured at the CERN nTOF facility from 1 eV to 1 MeV, covering the entire energy range of astrophysical interest. From these data Maxwellian averaged capture cross sections have been calculated with uncertainties between 3.3 and 4.7%. Additional information was obtained by measuring the inelastic scattering cross section of (187)Os at the Karlsruhe 3.7 MV Van de Graaff accelerator and by neutron resonance analyses of the nTOF capture data to establish a comprehensive experimental basis for the Hauser-Feshbach statistical model. Consistent I-IF calculations for the capture and inelastic reaction channels were performed to determine the stellar enhancement factors, which are required to correct the Maxwellian averaged cross sections for the effect of thermally populated excited states. The consequences of this analysis for the s-process component of the (187)Os abundance and the related impact on the evaluation of the time-duration of Galactic nucleosynthesis via the Re/Os cosmo-chronometer are discussed.