Context : The primordial nature of the Spite plateau is at odds with the WMAP satellite measurements , implying a primordial Li production at least three times higher than observed .
It has also been suggested that A ( Li ) might exhibit a positive correlation with metallicity below [ Fe/H ] \sim -2.5 .
Previous samples studied comprised few stars below [ Fe/H ] = - 3 .

Aims : We present VLT-UVES Li abundances of 28 Halo dwarf stars between [ Fe/H ] = - 2.5 and - 3.5 , ten of which have [ Fe/H ] < - 3 .

Methods : We determined stellar parameters and abundances using four different T { } _ { eff } scales .
The direct infrared flux method was applied to infrared photometry .
H \alpha wings were fitted with two synthetic grids computed by means of 1D LTE atmosphere models , assuming two different self-broadening theories .
A grid of H \alpha profiles was finally computed by means of 3D hydrodynamical atmosphere models .
The Li i doublet at 670.8 nm has been used to measure A ( Li ) by means of 3D hydrodynamical NLTE spectral syntheses .
An analytical fit of A ( Li ) _ { 3 D,NLTE } as a function of equivalent width , T { } _ { eff } , log g , and [ Fe/H ] has been derived and is made available .

Results : We confirm previous claims that A ( Li ) does not exhibit a plateau below [ Fe/H ] = - 3 .
We detect a strong positive correlation with [ Fe/H ] that is insensitive to the choice of T { } _ { eff } estimator .
From a linear fit , we infer a steep slope of about 0.30 dex in A ( Li ) per dex in [ Fe/H ] , which has a significance of 2-3 \sigma .
The slopes derived using the four T { } _ { eff } estimators are consistent to within 1 \sigma .
A significant slope is also detected in the A ( Li ) – T { } _ { eff } plane , driven mainly by the coolest stars in the sample ( T { } _ { eff } < 6250 ) , which appear to be Li-poor .
However , when we remove these stars the slope detected in the A ( Li ) – [ Fe/H ] plane is not altered significantly .
When the full sample is considered , the scatter in A ( Li ) increases by a factor of 2 towards lower metallicities , while the plateau appears very thin above [ Fe/H ] = - 2.8 .
At this metallicity , the plateau lies at \left \langle { A ( Li ) _ { 3 D,NLTE } } \right \rangle = 2.199 \pm 0.086 .

Conclusions : The meltdown of the Spite plateau below [ Fe/H ] \sim - 3 is established , but its cause is unclear .
If the primordial A ( Li ) were that derived from standard BBN , it appears difficult to envision a single depletion phenomenon producing a thin , metallicity independent plateau above [ Fe/H ] = - 2.8 , and a highly scattered , metallicity dependent distribution below .
That no star below [ Fe/H ] = - 3 lies above the plateau suggests that they formed at plateau level and experienced subsequent depletion .