  A gamma-ray burst (GRB) releases an amount of energy similar to that of a
supernova explosion, which combined with its rapid variability suggests an
origin related to neutron stars or black holes. Since these compact stellar
remnants form from the most massive stars not long after their birth, gamma-ray
bursts should trace the star formation rate in the Universe; we show that the
GRB flux distribution is consistent with this. Because of the strong evolution
of the star formation rate with redshift, it follows that the dimmest known
bursts have z ~ 6, much above the value usually quoted and beyond the most
distant quasars. This explains the absence of bright galaxies in well-studied
gamma-ray burst error boxes. The increased distances imply a peak luminosity of
8.3e51 erg/s and a rate density of 0.025 per million years per galaxy. These
values are 20 times higher and 150 times lower, respectively, than are implied
by fits with non-evolving GRB rates. This means that GRBs are either caused by
a much rarer phenomenon than mergers of binary neutron stars, or their
gamma-ray emission is often invisible to us due to beaming. Precise burst
locations from optical transients will discriminate between the various models
for GRBs from stellar deaths, because the distance between progenitor birth
place and burst varies greatly among them. The dimmest GRBs are then the most
distant known objects, and may probe the Universe at an age when the first
stars were forming.
