  Data from future high-precision Cosmic Microwave Background (CMB)
measurements will be sensitive to the primordial Helium abundance $Y_p$. At the
same time, this parameter can be predicted from Big Bang Nucleosynthesis (BBN)
as a function of the baryon and radiation densities, as well as a neutrino
chemical potential. We suggest to use this information to impose a
self-consistent BBN prior on $Y_p$ and determine its impact on parameter
inference from simulated Planck data. We find that this approach can
significantly improve bounds on cosmological parameters compared to an analysis
which treats $Y_p$ as a free parameter, if the neutrino chemical potential is
taken to vanish. We demonstrate that fixing the Helium fraction to an arbitrary
value can seriously bias parameter estimates. Under the assumption of
degenerate BBN (i.e., letting the neutrino chemical potential $\xi$ vary), the
BBN prior's constraining power is somewhat weakened, but nevertheless allows us
to constrain $\xi$ with an accuracy that rivals bounds inferred from present
data on light element abundances.
