Abstractω Centauri is a massive stellar system which is currently going through the Galactic Halo. Its compact aspect and spheroidal shape have for a long time led to it being classified as a Globular Cluster. However the fact that its stars cover a wide metallicity range (−0.6 < [Fe/H] < −2.1), points to this object as an external galaxy, satellite of the Milky Way. Lithium among warm metal-poor stars shows a roughly constant abundance, the “Spite Plateau”. This has been interpreted as evidence for a primordial origin of the lithium nucleus, at the time of nucleosynthesis. After the physical conditions under which nucleosynthesis occurred, have been constrained by the observations of the fluctuations of the Cosmic Microwave Background, we are facing a “cosmological lithium problem”, namely the primordial lithium was a factor of three to four higher than what observed in the Spite plateau. Several avenues may be taken to solve this conundrum, either relying on fundamental physics or on stellar physics, however the realm of possibilities may be considerably narrowed by observing stellar populations in different galaxies, which have experienced different evolutionary histories. Some of the proposed “solutions” may be clearly ruled out, depending on the observation of lithium in the metal-poor populations of external galaxies. ω Centauri is the only external galaxy amenable to such an investigation in the era of 8m telescopes. We have pushed to its limits FLAMES at the ESO 8.2m telescope to obtain high resolution spectra of the Li i doublet in 91 Turn-Off and Sub-Giant stars at V ~ 18 in ω Centauri. We present our preliminary results on this data which suggest that the Li content in ω Centauri warm stars is comparable to that observed in Galactic Halo field stars of similar metallicities and temperatures. This may effectively rule out a whole class of models which invoke a severe Li depletion through processing of material in an early generation of massive stars.