The rate of the hydrogen-burning carbon-nitrogen-oxygen (CNO) cycle is controlled by the slowest process, 14N(p,γ)15O, which proceeds by capture to the ground and several excited states in O15. Previous extrapolations for the ground state contribution disagreed by a factor 2, corresponding to 15% uncertainty in the total astrophysical S factor. At the Laboratory for Underground Nuclear Astrophysics (LUNA) 400 kV accelerator placed deep underground in the Gran Sasso facility in Italy, a new experiment on ground state capture has been carried out at 317.8, 334.4, and 353.3 keV center-of-mass energy. Systematic corrections have been reduced considerably with respect to previous studies by using a Clover detector and by adopting a relative analysis. The previous discrepancy has been resolved, and ground state capture no longer dominates the uncertainty of the total S factor. © 2008 The American Physical Society.