While the average metallicity of the intergalactic medium rises above Z~10^{-3} Zsun by the end of the reionization, pockets of metal-free gas can still exist at later times. We quantify the presence of a long tail in the formation rate of metal-free halos during late stages of reionization (redshift z~6), which might offer the best window to detect Population III stars. Using cosmological simulations for the growth of dark matter halos, coupled with analytical recipes for the metal enrichment of their interstellar medium, we show that pockets of metal-free gas exist at z~6 even under the assumption of high efficiency in metal pollution via winds. A comoving metal-free halo formation rate d^2n/dtdV > 10^{-9} Mpc^{-3}yr^{-1} is expected at z=6 for halos with virial temperature T_{vir}~10^4 K (mass ~10^8 Msun), sufficient to initiate cooling even with strong negative radiative feedback. Under the assumption of a single Population III supernova formed per metal-free halo, we expect an observed supernova rate of 2.6x10^{-3} deg^{-2}yr^{-1} in the same redshift range. These metal-free stars and their supernovae will be isolated and outside galaxies (at distances >150 h^{-1} kpc) and thus significantly less biased than the general population of ~10^8 Msun halos at z~6. Supernova searches for metal-free explosions must thus rely on large area surveys. If metal-free stars produce very luminous supernovae, like SN2006gy, then a multi-epoch survey reaching m_AB =27 at 1 micron is sufficient for detecting them at z=6. While the Large Synoptic Survey Telescope will not reach this depth in the z band, it will be able to detect several tens of Population III supernovae in the i and r bands at z <5.5, when their observed rate is down to 3-8x10^{-4} deg^{-2} yr^{-1}.
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