The neutron-rich 39 S nucleus has been studied using binary grazing reactions produced by the interaction of a 215-MeV beam of 36 S ions with a thin 208 Pb target. The magnetic spectrometer, PRISMA, and the γ -ray array, CLARA, were used in the measurements. Gamma-ray transitions of the following energies were observed: 339, 398, 466, 705, 1517, 1656, and 1724 keV. Five of the observed transitions have been tentatively assigned to the decay of excited states with spins up to (11/2 − ). The results of a state-of-the-art shell-model calculation of the level scheme of 39 S using the SDPF-U effective interaction are also presented. The systematic behavior of the excitation energy of the first 11/2 − states in the odd-A isotopes of sulfur and argon is discussed in relation to the excitation energy of the first excited 2 + states of the adjacent even-A isotopes. The states of 39 S that have the components in their wave functions corresponding to three neutrons in the 1f 7/2 orbital outside the N = 20 core have also been discussed within the context of the 0 ω shell-model calculations presented here.