  We show that the Supernovae results, implying evidence for an accelerating
Universe, may be closely related to the recent discovery of redshift dependence
in the fine structure constant $\alpha$. The link is a class of varying speed
of light (VSL) theories which contain cosmological solutions similar to
quintessence. During the radiation dominated epoch the cosmological constant
$\Lambda$ is prevented from dominating the Universe by the usual VSL mechanism.
In the matter epoch the varying c effects switch off, allowing $\Lambda$ to
eventually surface and lead to an accelerating Universe. By the time this
happens the residual variations in c imply a changing $\alpha$ at a rate that
is in agreement with observations.
