Context : We present the results of a dedicated search for extremely metal-poor stars in the Fornax , Sculptor , and Sextans dSphs . Five stars were selected from two earlier VLT/Giraffe and HET/HRS surveys and subsequently followed up at high spectroscopic resolution with VLT/UVES . All of them turned out to have [ Fe/H ] \lower 2.58 pt \hbox { $ \sim$ } \kern - 7.75 pt \raise 2.795 pt \hbox { $ < $ } -3 and three stars are below [ Fe/H ] \sim - 3.5 . This constitutes the first evidence that the classical dSphs Fornax and Sextans join Sculptor in containing extremely metal-poor stars and suggests that all of the classical dSphs contain extremely metal-poor stars . One giant in Sculptor at [ Fe/H ] = -3.96 \pm 0.06 is the most metal-poor star ever observed in an external galaxy . We carried out a detailed analysis of the chemical abundances of the \alpha , iron peak , and the heavy elements , and we performed a comparison with the Milky Way halo and the ultra faint dwarf stellar populations . Carbon , barium , and strontium show distinct features characterized by the early stages of galaxy formation and can constrain the origin of their nucleosynthesis . Aims : Methods : Results : Conclusions :