  Big Bang Nucleosynthesis can provide, via constraints on the expansion rate
at that time, limits on possible variations in Newton's Constant, $G$. The
original analyses were performed before an independent measurement of the
baryon-to-photon ratio from the cosmic microwave background was available.
Combining this with recent measurements of the primordial deuterium abundance
in quasar absorption systems now allows one to derive a new tighter constraint
on $G$ without recourse to considerations of helium or lithium abundances. We
find that, compared to todays value, $G_0$, $G_{BBN}/G_0=1.01^{+0.20}_{-0.16}$
at the 68.3% confidence level. If we assume a monotonic power law time
dependence, $G\propto t^{-\alpha}$, then the constraint on the index is $-0.004
< \alpha < 0.005$. This would translate into $-3\times10^{-13} \textrm{yr}^{-1}
< (\dot G/G)_{\textrm{today}} < 4 \times 10^{-13} \textrm{yr}^{-1}$.
