A new observation of D in a primordial gas cloud, made using the high-resolution spectrograph at the Keck telescope, indicates an abundance D/H = (1.9-2.5) x 10(-4) (Songaila et al. 1994). Because the new measurement is substantially larger than previous, Galactic estimates, this would force a reassessment of big bang nucleosynthesis (BBN) methodology and predictions-if it is confirmed. Using a new BBN Monte Carlo code and analysis technique (Kernan & Krauss 1994), we derive constraints implied by a lower limit of D/H = 1.9 x 10(-4). We find OMEGA(B) less-than-or-equal-to 0.0068 h-2, which is definitively incompatible with baryonic halo dark matter. We also explore implications of combining the D measurement with other light-element abundances. Li-7 provides a lower bound, OMEGA(B) greater-than-or-equal-to 0.004 h-2. Also, the initial He-4 mass fraction (Y(p)) would have to be less than 23.5%, assuming three light neutrino species-in good agreement with present observational estimates. Finally, observational upper limits of Y(p) less-than-or-equal-to 24% and Li-7/H less-than-or-equal-to 2.3 x 10(-10) would now allow the number of effective neutrino species to be as large as 3.9.