  We investigate the cosmological consequences of a simple theory in which the
electric charge $e$ is allowed to vary. The theory is locally gauge and Lorentz
invariant, and satisfies general covariance. We find that in this theory the
fine structure 'constant', $\alpha $, remains almost constant in the radiation
era, undergoes small increase in the matter era, but approaches a constant
value when the universe starts accelerating because of the presence of a
positive cosmological constant. This model satisfies geonuclear,
nucleosynthesis, and CMB constraints on time-variation in $\alpha $, while
fitting simultaneously the observed accelerating universe and the recent
high-redshift evidence for small $\alpha $ variations in quasar spectra. The
model also places specific restrictions on the nature of the dark matter.
Further tests, involving stellar spectra and the E\"otv\"os experiment, are
proposed.
