We present a new analysis of an absorption system in the spectrum of Q0014+813, with particular attention to a single cold cloud at redshift z=2.797957. Features are identified at this redshift corresponding to Si III, Si IV, C IV, D I, and H I, all consistent with purely thermal broadening at T approximate to 19,000 K. The deuterium identification is confirmed by its narrow width and precise agreement with the silicon and carbon redshifts. The H I column is well constrained by a slightly damped profile in the blue wing of Ly alpha, and the D I column by its saturation, leading to a 95% confidence lower limit (D/H)>0.7X10(-4). The abundance is measured from line fits to be (D/H)=1.9(-0.9)(+1.6)x10(-4), in agreement with the high deuterium abundance previously found in the z=3.32 system in the same quasar spectrum. This system strengthens the case for a high universal primordial deuterium abundance and low cosmic baryon density (eta=1.7X10(-10), Omega(b)h(2)=0.006), for which Standard Big Bang Nucleosynthesis gives concordant predictions for helium-4 and lithium-7 abundances. Implications for Galactic chemical evolution and the baryonic and nonbaryonic dark matter problems are briefly discussed. (C) 1996 American Astronomical Society.