Greigite (Fe3S4), a widely occurring iron thiospinel, was investigated using soft X-ray absorption spectroscopy (XAS) and X-ray magnetic circular dichroism (XMCD). XAS and XMCD spectra were recorded at the Fe L2,3 edges for pure synthetic and natural greigite samples. At the Fe L3 edge, the XAS spectra reveal two main absorption peaks at 707.2 and 708.6 eV, which are interpreted to originate from greigite and an oxidized surface layer on greigite crystals. The XMCD spectra, which are dominated by a greigite signal, contain three peaks at 705.3, 706.2, and 707.7 eV, all with the same sign. The expectation is that the spectrum would have two negative peaks representing Fe2+ and Fe3+ in octahedral coordination, and a positive peak representing Fe3+ in tetrahedral coordination, as found in stoichiometric magnetite (Fe3O4). A reasonable fit of the XMCD data can be achieved without the tetrahedral Fe component, which contradicts magnetic structural information provided by neutron diffraction analysis, and uses unreasonable parameters. The conundrum between theory and experimental data may be caused by the strong covalent effect in sulfides, which causes broadening of the hybridized XMCD peaks and also indicates that multiplet calculations cannot fully predict the properties of greigite. Our results indicate covalent 3d states in greigite, which can destroy the half-metallicity that is present in magnetite. Our measurements represent the best available XAS and XMCD spectra for greigite, but further experimental and modeling information are needed to explain the observed XMCD spectra and to understand what it represents in terms of electronic and magnetic structure. This is important because greigite widely contributes to the magnetic properties of sedimentary rocks.