  Growing theoretical evidence suggests that the first generation of stars may
have been quite massive (~100-300 solar masses). If they retain their high mass
until death, such stars will, after about 3Myr, make pair-instability
supernovae. We consider the complete evolution of two zero-metallicity stars of
250 and 300 solar masses. Explosive oxygen and silicon burning cause the 130
solar mass helium core to explode, but explosive burning is unable to drive an
explosion in the 300 solar mass star and it collapses to a black hole. For this
star, the calculated angular momentum in the presupernova model is sufficient
to delay black hole formation and the star initially forms a 50 solar mass,
1000km core within which neutrinos are trapped. Although the star does not
become dynamically unstable, the calculated growth time of secular rotational
instabilities is shorter than the black hole formation time, and such
instabilities may develop. We estimate the energy and amplitude of the
gravitational waves emitted during this collapse. After the black hole forms,
accretion continues through a disk. Although the disk is far too large and cool
to transport energy efficiently to the rotational axis by neutrino
annihilation, it has ample potential energy to produce a 1e54erg jet driven by
magnetic fields. The interaction of this jet with surrounding circumstellar gas
may produce an energetic gamma-ray transient, but given the redshift and time
scale, this is probably not a model for typical gamma-ray bursts.
