The metal-poor (Z ≃ 1/100 Z⊙) damped Lyman α system (DLA) at redshift zabs = 3.049 84 in the zem ≃ 3.030 QSO SDSS J1419+0829 has near-ideal properties for an accurate determination of the primordial abundance of deuterium (D/H)p. We have analysed a high-quality spectrum of this object with software specifically designed to deduce the best-fitting value of D/H and to assess comprehensively the random and systematic errors affecting this determination. We find (D/H)DLA = (2.535 ± 0.05) × 10−5, which in turn implies Ωb, 0h2 = 0.0223 ± 0.0009, in very good agreement with Ωb, 0h2(CMB) = 0.0222 ± 0.0004 deduced from the angular power spectrum of the cosmic microwave background (CMB). If the value in this DLA is indeed the true (D/H)p produced by big bang nucleosynthesis (BBN), there may be no need to invoke non-standard physics nor early astration of D to bring together Ωb, 0 h2(BBN) and Ωb, 0 h2(CMB). The scatter between most of the reported values of (D/H)p in the literature may be due largely to unaccounted systematic errors and biases. Further progress in this area will require a homogeneous set of data comparable to those reported here and analysed in a self-consistent manner. Such an endeavour, while observationally demanding, has the potential of improving our understanding of BBN physics, including the relevant nuclear reactions, and the subsequent processing of light nuclides through stars.