THE primordial ratio of deuterium to hydrogen nuclei (D/H), created as a result of the Big Bang, provides the most sensitive measure of the cosmological density of baryons(1-5). Measurements of the D/H ratio in the interstellar medium of our Galaxy place a strict lower limit on the primordial ratio(6), because processing of gas by stars reduces the abundance of deuterium relative to hydrogen. Absorption of radiation from distant quasars by intervening clouds of gas offers a means of probing D/H ratios at large redshifts, where the effects of stellar processing should be negligible. Measurements(7,8) on one absorption system have indicated an extremely high primordial abundance ratio of 24 x 10(-5). Here we report a measurement of the D/H ratio in another high-redshift absorption system, and obtain a value that is an order of magnitude lower than that reported previously(7,8). The measured ratio of 2.3 x 10(-5) is consistent with that in the interstellar medium (after allowing for Galactic chemical evolution(9,10)), and indicates that the absorption spectra on which the earlier estimates are based may have been subject to strong contamination. We calculate a baryon density that is 5% of the critical density required to close the Universe.