A detailed calculation of element production in the early stages of a homogeneous and isotropic expanding universe as well as within imploding-exploding supermassive stars has been made. If the recently measured microwave background radiation is due to primeval photons, then significant quantities of only D, He3, He4, and Li7 can be produced in the universal fireball. Reasonable agreement with solar- system abundances for these nuclei is obtained if the present temperature is 3 K and if the present density is 2 X 10-" gm cm', corresponding to a deceleration parameter qo 5 X 10-'. However, massive stars "bouncing" at temperatures 10 K can convert the universal D and He3 into C, N, 0, Ne, Mg, and some heavier elements in amounts observed in the oldest stars. The mass gaps at A = 5 and 8 are bridged by the reactions He' (He4, )Be7(He4, ) C11. Bounces at higher temperatures bridge the mass gaps through 3 He4 H C12 and mainly produce metals of the iron group, plus a small amount of heavier elements synthesized by a new kind of r-process (rapid neutron capture). It is found that very low abundances of He4, as recently observed in some stars, can be produced in a universe in which the electron neutrinos are degenerate.