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Detection of gamma-ray bursts (GRBs) from redshifts z > 7 would open a new window into the earliest epoch of cosmic star formation. We construct separate star formation histories at high redshifts for normal (Pop I and II) stars, and for predominantly massive (Pop III) stars. Based on these separate histories, we predict the GRB redshift distribution to be observed by the Swift mission. Regardless of whether Pop III progenitors are able to trigger GRBs, we find that a fraction 10 at z > 5. Thisdoi:10.1086/500799 fatcat:gv6ehk536bd7pcbpw57bkj7pti