  We estimate the maximum contribution to reionization from the first
generation of massive stars, with zero metallicity, under the assumption that
one of these stars forms with a fixed mass in every collapsed halo in which
metal-free gas is able to cool. We assume that any halo that has already had
stars previously formed in one of their halo progenitors will form only stars
with metals, which are assigned an emissivity of ionizing radiation equal to
that determined at z=4 from the measured intensity of the ionizing background.
We examine the impact of molecular hydrogen photodissociation (which tends to
reduce cooling when a photodissociating background is produced by the first
stars) and X-Ray photoheating (which heats the atomic medium, raising the
entropy of the gas before it collapses into halos). We find that in the
CDM$\Lambda$ model supported by present observations, and even assuming no
negative feedbacks for the formation of metal-free stars, a reionized mass
fraction of 50% is not reached until redshift $z\sim 12$. The combination of
ordinary metal-enriched stars and early metal-free stars can yield a CMB
optical depth to electron scattering of at most 0.13. The contribution of
metal-free stars to the present Cosmic Infrarred Background is negligibly
small.
