  We present a new measurement of the deuterium-to-hydrogen ratio (D/H) in the
Lyman limit absorption system at $z = 3.572$ towards Q1937--1009. We use an
improved method to measure D/H in QSO absorption systems, which includes extra
parameters to treat the continuum uncertainties, a variety of new absorption
models which allow for undetected velocity structure, and the improved
measurement of the total hydrogen column density by Burles & Tytler (1997a). We
find that all models, including contamination, give an upper limit D/H $< 3.9
\times 10^{-5}$ (95 % confidence). Both this and previous analyses find
contamination to be unlikely in this absorption system, A $\chi^2$ analysis in
models without contamination gives D/H $= 3.3 \pm 0.3 \times 10^{-5}$ (67%
confidence), which is higher but consistent with the earlier results of Tytler
et al. (1996), and a second measurement of D/H towards Q1009+2956 (Burles &
Tytler 1997). With calculations of standard big bang nucleosynthesis (SBBN) and
the assumption that this measurement of D/H is representative of the primordial
value, we find a high baryon-to-photon ratio, $\eta = 5.3 \pm 0.4 \times
10^{-10}$. This is consistent with primordial abundance determinations of
$^4$He in H II regions (Izotov et al. 1997) and $^7$Li in the atmospheres of
warm metal-poor population II stars (Bonifacio & Molaro 1997). We find a high
value for the present-day baryon density, $\Omega_b h^2 = 0.0193 \pm 0.0014$,
which is consistent with other inventories of baryonic matter, from low to high
redshift: clusters of galaxies, the Lyman alpha forest & the Cosmic Microwave
Background.
