  Within the context of mass-varying neutrinos, we construct a cosmological
model that has a phase transition in the electromagnetic fine structure
constant \alpha at a redshift of 0.5. The model accommodates hints of a time
variable \alpha in quasar spectra and the nonobservance of such an effect at
very low redshifts. It is consistent with limits from the recombination and
primordial nucleosynthesis eras and is free of instabilities.
