  We predict the redshift of the first observable (i.e., in our past light
cone) Gamma Ray Burst (GRB) and calculate the GRB-rate redshift distribution of
the Population III stars at very early times (z=20-60). Using the last 2 years
of data from Swift we place an upper limit on the efficiency (\eta_{GRB}) of
GRB production per solar mass from the first generation of stars. We find that
the first observable GRB is most likely to have formed at redshift 60. The
observed rate of extremely high redshift GRBs (XRGs) is a subset of a group of
15 long GRBs per year, with no associated redshift and no optical afterglow
counterparts, detected by Swift. Taking this maximal rate we get that
\eta_{GRB}<1.1~10^{-4} GRBs per solar mass in stars. A more realistic
evaluation, e.g., taking a subgroup of 5% of the total sample of Swift gives an
upper limit of \eta_{GRB}<3.2~10^{-5} GRBs per solar mass.
