Context : Unevolved metal-poor stars constitute a fossil record of the Early Galaxy , and can provide invaluable information on the properties of the first generations of stars .
Binary systems also provide direct information on the stellar masses of their member stars .

Aims : The purpose of this investigation is a detailed abundance study of the double-lined spectroscopic binary CS 22876–032 , which comprises the two most metal-poor dwarfs known .

Methods : We have used high-resolution , high-S/N ratio spectra from the UVES spectrograph at the ESO VLT telescope .
Long-term radial-velocity measurements and broad-band photometry allow us to determine improved orbital elements and stellar parameters for both components .
We use OSMARCS 1D models and the turbospectrum spectral synthesis code to determine the abundances of Li , O , Na , Mg , Al , Si , Ca , Sc , Ti , Cr , Mn , Fe , Co and Ni .
We also use the CO ^ { 5 } BOLD model atmosphere code to compute the 3D abundance corrections , especially for Li and O .

Results : We find a metallicity of [ Fe/H ] \sim - 3.6 for both stars , using 1D models with 3D corrections of \sim - 0.1 dex from averaged 3D models .
We determine the oxygen abundance from the near-UV OH bands ; the 3D corrections are large , -1 and -1.5 dex for the secondary and primary respectively , and yield [ O/Fe ] \sim 0.8 , close to the high-quality results obtained from the [ OI ] 630 nm line in metal-poor giants .
Other [ \alpha /Fe ] ratios are consistent with those measured in other dwarfs and giants with similar [ Fe/H ] , although Ca and Si are somewhat low ( [ X/Fe ] \la 0 ) .
Other element ratios follow those of other halo stars .
The Li abundance of the primary star is consistent with the Spite plateau , but the secondary shows a lower abundance ; 3D corrections are small .

Conclusions : The Li abundance in the primary star supports the extension of the Spite Plateau value at the lowest metallicities , without any decrease .
The low abundance in the secondary star could be explained by endogenic Li depletion , due to its cooler temperature .
If this is not the case , another , yet unknown mechanism may be causing increased scatter in A ( Li ) at the lowest metallicities .