  We examine Big Bang nucleosynthesis (BBN) in the case of inhomogenous
neutrino degeneracy, in the limit where the fluctuations are sufficiently small
on large length scales that the present-day element abundances are homogeneous.
We consider two representive cases: degeneracy of the electron neutrino alone,
and equal chemical potentials for all three neutrinos. We use a linear
programming method to constrain an arbitrary distribution of the chemical
potentials. For the current set of (highly-restrictive) limits on the
primordial element abundances, homogeneous neutrino degeneracy barely changes
the allowed range of the baryon-to-photon ratio. Inhomogeneous degeneracy
allows for little change in the lower bound on the baryon-to-photon ratio, but
the upper bound in this case can be as large as 1.1 \times 10^{-8} (only
electron neutrino degeneracy) or 1.0 \times 10^{-9} (equal degeneracies for all
three neutrinos). For the case of inhomogeneous neutrino degeneracy, we show
that there is no BBN upper bound on the neutrino energy density, which is
bounded in this case only by limits from structure formation and the cosmic
microwave background.
