  A variation of the fundamental constants is expected to affect the
thermonuclear rates important for stellar nucleosynthesis. In particular,
because of the very small resonant energies of Be8 and C12, the triple $\alpha$
process is extremely sensitive to any such variations. Using a microscopic
model for these nuclei, we derive the sensitivity of the Hoyle state to the
nucleon-nucleon potential allowing for a change in the magnitude of the nuclear
interaction. We follow the evolution of 15 and 60 solar mass, zero metallicity
stellar models, up to the end of core helium burning. These stars are assumed
to be representative of the first, Population III stars. We derive limits on
the variation of the magnitude of the nuclear interaction and model dependent
limits on the variation of the fine structure constant based on the calculated
oxygen and carbon abundances resulting from helium burning. The requirement
that some C12 and O16 be present are the end of the helium burning phase allows
for permille limits on the change of the nuclear interaction and limits of
order 10^{-5} on the fine structure constant relevant at a cosmological
redshift of z ~ 15-20.
