The primordial ratio of the number of deuterium to hydrogen nuclei (D/H) created in big bang nucleosynthesis is the most sensitive measure of the cosmological baryon to photon ratio and the cosmological density of baryons Ω b (1-5). In the interstellar medium (ISM) of our Galaxy D/H = 1.6 ± 0.1 × 10 −5 (6), which places a strict lower limit on the primordial abundance, because stars reduce the proportion of D in the ISM. Quasar absorption systems (QAS) should give definitive measurements of the primordial D because they can sample metal-poor gas at early epochs where the destruction of D should be negligible. A probable measurement of a high abundance ratio was reported in one QAS: D/H ≈ 24 × 10 −5 (7,8). Here we report a measurement of low D/H = 2.3 ×10 −5 , in another QAS, which is consistent with D/H in the ISM, with models of Galactic chemical evolution, (9,10), and with earlier data (7,8) provided that D line is strongly contaminated. We have internal consistency checks, and believe that this is the first direct measurement of a primordial abundance ratio. It provides the most accurate measurement of the baryon density: a high value of Ω b = 0.05, assuming a Hubble constant H 0 = 70 km s −1 Mpc −1 .Deuterium is rarely seen in QAS because the associated hydrogen is usually distributed over a wide range of velocities and its absorption covers deuterium. We selected QSO 1937-1009 because we found that the absorption system at z = 3.572 showed unusually weak metal lines in low resolution spectra, which we took to indicate that the gas was distributed in one or two narrow velocity components (11). We obtained optical spectra of QSO 1937-1009 (z em = 3.78, V ≃ 17.5) with the HIRES echelle spectrograph (12) on the W. M. Keck 10-m telescope. The high quality spectra make this amongst the best characterized QAS, and show strong absorption at the expected position of the D Lyα line and weak but highly significant absorption at D Lyβ .The weak metal lines in the system, C II, C IV, Si II, and Si IV, appear to have the same profiles, which are adequately described by two components separated by 15 km s −1 .