  Recent determinations of the deuterium abundance, $^2$H/H, in high redshift
Lyman limit hydrogen clouds challenge the usual picture of primordial
nucleosynthesis based on \lq\lq concordance\rq\rq\ of the calculated light
element ($^2$H, $^3$He, $^4$He, $^7$Li) nucleosynthesis yields with the
observationally-inferred abundances of these species. Concordance implies that
all light element yields can be made to agree with the observationally-inferred
abundances (within errors) for single global specifications of the
baryon-to-photon ratio, $\eta$; lepton number; neutron lifetime; and expansion
rate (or equivalently, effective number of light neutrino degrees of freedom
$N_{\nu} $). Though one group studying Lyman limit systems obtains a high value
of $^2$H/H ($\sim 2\times {10}^{-4}$), another group finds consistently low
values ($\sim 2\times {10}^{-5}$). In the former case, concordance for $N_{\nu}
=3$ is readily attained for the current observationally-inferred abundances of
$^4$He and $^7$Li. But if the latter case represents the primordial deuterium
abundance, then concordance for {\it any} $N_{\nu}$ is impossible unless the
primordial value of $^7$Li/H is considerably larger than the abundance of
lithium as measured in old, hot Pop II halo stars. Furthermore, concordance
with $N_{\nu}=3$ is possible for low $^2$H/H only if either (1) the primordial
$^4$He abundance has been significantly underestimated, or (2) new neutrino
sector physics is invoked. We argue that systematic underestimation of both the
$^7$Li and $^4$He primordial abundances is the likely resolution of this
problem, a conclusion which is strengthened by new results on $^4$He.
