  Since the pioneering observations of Spite & Spite in 1982, the constant
lithium abundance of metal-poor ([Fe/H]<-1.3) halo stars near the turnoff has
been attributed a cosmological origin. Closer analysis revealed that the
observed abundance lies at $\Delta$ Li~0.4 dex below the predictions of Big
Bang Nucleosynthesis. The measurements of deuterium abundances on the lines of
sight toward quasars and the recent data from the Wilkinson Microwave
Anisotropy Probe independently confirmed this gap. We suggest here that part of
the discrepancy is explained by the first generation of stars that efficiently
depleted lithium. Assuming that the models for lithium evolution in the halo
turnoff stars and $\Delta$ Li estimates are correct, we infer that between 1/3
and 1/2 of the baryonic matter of the early halo (~10^9 Mo) was processed
through Population III stars. This new paradigm proposes a very economical
solution to the lingering difficulty of understanding the properties of the
Spite Plateau and its lack of star-to-star scatter down to [Fe/H]=-2.5. It is
moreover in agreement both with the absence of lithium detection in the most
metal-poor star presently known (HE 1327-2326), and also with new trends of the
Plateau suggesting its low metallicity edge may be reached around [Fe/H]=-2.5.
We discuss the turbulent mixing associated with enhanced supernovae explosions
in the early interstellar medium in this picture. Finally we show that other
chemical properties of the extremely metal-poor stars are in agreement with a
significant Population III processing in the halo, provided these models
include mass-loss and rotationally-induced mixing.
