Context : A discrepancy has emerged between the cosmic lithium abundance inferred by the WMAP satellite measurement coupled with the prediction of the standard big-bang nucleosynthesis theory , and the constant Li abundance measured in metal-poor halo dwarf stars ( the so-called Spite plateau ) . Several models are being proposed to explain this discrepancy , involving either new physics , in situ depletion , or the efficient depletion of Li in the pristine Galaxy by a generation of massive first stars . The realm of possibilities may be narrowed considerably by observing stellar populations in different galaxies , which have experienced different evolutionary histories . Aims : The \omega  Centauri stellar system is commonly considered as the remnant of a dwarf galaxy accreted by the Milky Way . We investigate the lithium content of a conspicuous sample of unevolved stars in this object . Methods : We obtained moderate resolution ( R=17 000 ) spectra for 91 main-sequence/early sub-giant branch ( MS/SGB ) \omega  Cen stars using the FLAMES-GIRAFFE/VLT spectrograph . Lithium abundances were derived by matching the equivalent width of the Li i resonance doublet at 6708 à to the prediction of synthetic spectra computed with different Li abundances . Synthetic spectra were computed using the SYNTHE code along with ATLAS–9 model atmospheres . The stars effective temperatures are derived by fitting the wings of the H _ { \alpha } line with synthetic profiles . Results : We obtain a mean content of A ( Li ) =2.19 \pm 0.14 dex for \omega Centauri MS/SGB stars . This is comparable to what is observed in Galactic halo field stars of similar metallicities and temperatures . Conclusions : The Spite plateau seems to be an ubiquitous feature of old , warm metal-poor stars . It exists also in external galaxies , if we accept the current view about the origin of \omega  Cen . This implies that the mechanism ( s ) that causes the “ cosmological lithium problem ” may be the same in the Milky Way and other galaxies .