  We discuss constraints on so-called `varying speed of light theories' coming
from the physics of the early universe. Specifically, we consider the position
of the first acoustic peak of the CMB angular power spectrum, showing that the
recent determination of its position by various CMB experiments, in particular
BOOMERanG/NA, can be used to constrain the value of the speed of light $c$
after the epoch of last scattering. Specifically, we find that for a flat
universe and a standard density of baryonic matter a variation in $c$ of up to
4% is consistent with the current observations. The position of the Doppler
peak is fairly sensitive to changes in $c$, and future observations should
dramatically improve this bound. On the other hand, we also find that the
maximum baryonic density allowed in VSL theories is about $\Omega_B h^2\sim
0.06\Omega_0$. We comment on the significance of these results.
