  We study the evolution of first star (Population III) binaries. Under
specific conditions, these stars may produce high redshift gamma-ray bursts
(GRBs). We demonstrate that the occurrence rate of GRBs does not depend
sensitively on evolutionary parameters in the population synthesis models. We
show that the first binaries may form a very small group (< 1%) of fast
rotating stars through binary tidal interactions that make GRBs. This finding
is contrary to the Bromm & Loeb assumption that all stars in close Population
III binaries will be spun up by tides and produce a GRB. We find that there is
simply not enough fast rotating stars in Population III binaries to expect
detection with SWIFT. Predicted detection rates, even with very optimistic
assumptions on binary fraction, evolutionary parameters and GRB detection, are
very small: 0.1-0.01 per year.
