A local structure study of ZnS nanocrystals, doped with very low concentrations of Cu, was carried out using the EXAFS technique to better understand how Cu substitutes into the host lattice and forms Cu luminescence centers. We show that a large fraction of the Cu have three nearest neighbor S atoms and the Cu-S bond is significantly shortened compared to Zn-S, by ∼0.08 Å. In addition, the second neighbor Cu-Cu peak is extremely small. We propose that Cu occupies an interior site next to a S(2-) vacancy, with the Cu displaced towards the remaining S(2-) and away from the vacancy; such a displacement immediately explains the lack of a significant Cu-Cu peak in the data. There is no evidence for interstitial Cu sites (Cu(i)), indicating that no more than 2% of the Cu are Cu(i.) This study provides new insights into the local structure of the Cu dopant in ZnS without the presence of CuS nanoprecipitates that are present at higher Cu doping levels.