We consider the stochastic background of gravitational waves produced by an early generation of Population III stars coupled with a normal mode of star formation at lower redshift. The computation is performed in the framework of hierarchical structure formation and is based on cosmic star formation histories constrained to reproduce the observed star formation rate at redshift $z \la 6$, the observed chemical abundances in damped Lyman alpha absorbers and in the intergalactic medium, and to allow for an early reionization of the Universe at $z\sim 10-20$ as indicated by the first year results released by WMAP. We find that the normal mode of star formation produces a gravitational wave background which peaks at 300-500 Hz and is within LIGO III sensitivity. The Population III component peaks at lower frequencies (30-100 Hz depending on the model), and could be detected by LIGO III as well as the planned BBO and DECIGO interferometers.

16 pages, 8 figures