  We have used recent observations of helium-4, nitrogen and oxygen from some
four dozen, low metallicity, extra-galactic HII regions to define mean $N$
versus $O$, $^4He$ versus $N$ and $^4He$ versus $O$ relations which are
extrapolated to zero metallicity to determine the primordial $^4He$ mass
fraction $Y_P$. The data and various subsets of the data, selected on the basis
of nitrogen and oxygen, are all consistent with $Y_P = 0.232 \pm 0.003$. For
the 2$\sigma$ (statistical) upper bound we find $Y_P^{2\sigma} \le 0.238$.
Estimating a 2\% systematic uncertainty $(\sigma _{syst} = \pm 0.005)$ leads to
a maximum upper bound to the primordial helium mass fraction: $Y_P^{MAX} =
Y_P^{2\sigma} + \sigma_{syst} \le 0.243$. We compare these upper bounds to
$Y_P$ with recent calculations of the predicted yield from big bang
nucleosynthesis to derive upper bounds to the nucleon-to-photon ratio $\eta$
($\eta_{10} \equiv 10^{10}\eta$) and the number of equivalent light (\lsim 10
MeV) neutrino species. For $Y_P \le 0.238$ ($0.243$), we find $\eta_{10} \le
2.5 (3.9)$ and $N_\nu \leq 2.7 (3.1)$. If indeed $Y_P \le 0.238$, then BBN
predicts enhanced production of deuterium and helium-3 which may be in conflict
with the primordial abundances inferred from model dependent (chemical
evolution) extrapolations of solar system and interstellar observations. Better
chemical evolution models and more data - especially $D$-absorption in the QSO
Ly-$\alpha$ clouds - will be crucial to resolve this potential crisis for BBN.
The larger upper bound, $Y_P \leq 0.243$ is completely
