Enstatite meteorites include the undifferentiated enstatite chondrites and the differentiated enstatite achondrites (aubrites). They are the most reduced group of all meteorites. The oxygen isotope compositions of both enstatite chondrites and aubrites plot along the terrestrial mass fractionation line, which suggests some genetic links between these meteorites and the Earth as well. For this study, we measured the Zn isotopic composition of 25 samples from the following groups: aubrites (main group and Shallowater), EL chondrites, EH chondrites and Happy Canyon (impact-melt breccia). We also analyzed the Zn isotopic composition and elemental abundance in separated phases (metal, silicates, and sulfides) of the EH4, EL3, and EL6 chondrites. The different groups of meteorites are isotopically distinct and give the following values (‰): aubrite main group (-7.08<δ66Zn<-0.37); EH3 chondrites (0.15<δ66Zn<0.31); EH4 chondrites (0.15<δ66Zn<0.27); EH5 chondrites (δ66Zn=0.27±0.09; n=1); EL3 chondrites (0.01<δ66Zn<0.63); the Shallowater aubrite (1.48<δ66Zn<2.36); EL6 chondrites (2.26<δ66Zn<7.35); and the impact-melt enstatite chondrite Happy Canyon (δ66Zn=0.37).The aubrite Peña Blanca Spring (δ66Zn=-7.04‰) and the EL6 North West Forrest (δ66Zn=7.35‰) are the isotopically lightest and heaviest samples, respectively, known so far in the Solar System. In comparison, the range of Zn isotopic composition of chondrites and terrestrial samples (-1.5<δ66Zn<1‰) is much smaller (Luck et al., 2005; Herzog et al., 2009).EH and EL3 chondrites have the same Zn isotopic composition as the Earth, which is another example of the isotopic similarity between Earth and enstatite chondrites. The Zn isotopic composition and abundance strongly support that the origin of the volatile element depletion between EL3 and EL6 chondrites is due to volatilization, probably during thermal metamorphism. Aubrites show strong elemental depletion in Zn compared to both EH and EL chondrites and they are enriched in light isotopes (δ66Zn down to -7.04‰). This is the opposite of what would be expected if Zn elemental depletion was due to evaporation, assuming the aubrites started with an enstatite chondrite-like Zn isotopic composition. Evaporation is therefore not responsible for volatile loss from aubrites. On Earth, Zn isotopes fractionate very little during igneous processes, while differentiated meteorites show only minimal Zn isotopic variability. It is therefore very unlikely that igneous processes can account for the large isotopic fractionation of Zn in aubrites. Condensation of an isotopically light vapor best explains Zn depletion and isotopically light Zn in these puzzling rocks. Mass balance suggests that this isotopically light vapor carries Zn lost by the EL6 parent body during thermal metamorphism and that aubrites evolved from an EL6-like parent body. Finally, Zn isotopes suggest that Shallowater and aubrites originate from distinct parent bodies.