  We report a reanalysis of a near-pristine absorption system, located at a
redshift z_abs=2.52564 toward the quasar Q1243+307, based on the combination of
archival and new data obtained with the HIRES echelle spectrograph on the Keck
telescope. This absorption system, which has an oxygen abundance
[O/H]=-2.769+/-0.028 (~1/600 of the Solar abundance), is among the lowest
metallicity systems currently known where a precise measurement of the
deuterium abundance is afforded. Our detailed analysis of this system
concludes, on the basis of eight D I absorption lines, that the deuterium
abundance of this gas cloud is log_10(D/H) = -4.622+/-0.015, which is in very
good agreement with the results previously reported by Kirkman et al. (2003),
but with an improvement on the precision of this single measurement by a factor
of ~3.5. Combining this new estimate with our previous sample of six high
precision and homogeneously analyzed D/H measurements, we deduce that the
primordial deuterium abundance is log_10(D/H)_P = -4.5974+/-0.0052 or,
expressed as a linear quantity, (D/H)_P = (2.527+/-0.030)x10^-5; this value
corresponds to a one percent determination of the primordial deuterium
abundance. Combining our result with a BBN calculation that uses the latest
nuclear physics input, we find that the baryon density derived from BBN agrees
to within 2 sigma of the latest results from the Planck CMB data.
