  If Gamma-Ray-Bursts (GRBs) occur at high redshifts, then their bright
afterglow emission can be used to probe the ionization and metal enrichment
histories of the intervening intergalactic medium during the epoch of
reionization. In contrast to other sources, such as galaxies or quasars, which
fade rapidly with increasing redshift, the observed infrared flux from a GRB
afterglow at a fixed observed age is only a weak function of its redshift. This
results from a combination of the spectral slope of GRB afterglows and the
time-stretching of their evolution in the observer's frame. Assuming that the
GRB rate is proportional to the star formation rate and that the characteristic
energy output of GRBs is ~10^{52} ergs, we predict that there are always ~15
GRBs from redshifts z>5 across the sky which are brighter than ~100 nJy at an
observed wavelength of ~2 \mu m. The infrared spectrum of these sources could
be taken with the future Next Generation Space Telescope, as a follow-up on
their early X-ray localization with the Swift satellite.
