The Se-78(n, gamma)Se-79 cross section has a high impact on the abundances of Se-78 produced during the slow neutron capture process (s process) in massive stars. A measurement of the Se-78 radiative neutron capture cross section has been performed at the Neutron Time-of-Flight facility at CERN using a set of liquid scintillation detectors that have been optimized for a low sensitivity to neutrons. We present resonance capture kernels up to 70 keV and cross section from 70 to 600 keV. Maxwellian-averaged cross section (MACS) values were calculated for stellar temperatures between kT = 5 and 100 keV, with uncertainties between 4.6% and 5.8%. The new MACS values result in substantial decreases of 20-30% of Se-78 abundances produced in the s process in massive stars and AGB stars. Massive stars are now predicted to produce subsolar Se-78/Se-76 ratios, which is expected since Se-76 is an s-only isotope, while solar Se-78 abundances have also contributions from other nucleosynthesis processes.