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 intuitive notion that the majority of stars in close Population III binaries will be sufficiently spun up by tides to produce a GRB. We find that there are simply not enough fast-rotating stars in Population III binaries to expect them to be detected with Swift. Predicted detection rates, even with very optimistic assumptions for the binary fraction, evolutionary parameters, and GRB detection, are very small: ~0.1-0.01 yr-1.