The -decay of 187Re (t1/2 = 42.3 Gyr) represents a suited cosmo-chronometer for the age of the r-process abundances, since the radiogenic part of the daughter isotope 187Os is defined by the difference between the solar 187Os abundance and s-process contribution to 187Os. The latter component can be determined via the s-process systematics based on the stellar neutron capture cross sections of 186Os and 187Os. The laboratory cross section of 187Os requires a significant correction for the effect of the low-lying excited state at 9.75 keV, which is strongly populated under stellar conditions. This theoretical correction can be improved by an experimental cross section for inelastic scattering to the 9.75 keV state. High resolution time-of-flight measurements of (n, ) cross sections of 186,187,188Os from 1 eV to 1 MeV at CERN n TOF facility are reported. The inferred stellar cross sections differ from previously recommended values. In addition, the inelastic scattering cross section has been measured at 30 keV neutron energy via time-of-flight at the Karlsruhe 3.7 MV Van de Graaff. The implications of these results for the Re/Os clock are discussed.