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

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... ars 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.