  Those massive stars that, during their deaths, give rise to gamma-ray bursts
(GRBs) must be endowed with an unusually large amount of angular momentum in
their inner regions, one to two orders of magnitude greater than the ones that
make common pulsars. Yet the inclusion of mass loss and angular momentum
transport by magnetic torques during the precollapse evolution is known to sap
the core of the necessary rotation. Here we explore the evolution of very
rapidly rotating, massive stars, including stripped down helium cores that
might result from mergers or mass transfer in a binary, and single stars that
rotate unusually rapidly on the main sequence. For the highest possible
rotation rates (about 400 km/s), a novel sort of evolution is encountered in
which single stars mix completely on the main sequence, never becoming red
giants. Such stars, essentially massive "blue stragglers", produce
helium-oxygen cores that rotate unusually rapidly. Such stars might comprise
roughly 1% of all stars above 10 solar masses and can, under certain
circumstances retain enough angular momentum to make GRBs. Because this
possibility is very sensitive to mass loss, GRBs will be much more probable in
regions of low metallicity.
