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.
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