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Intergalactic gas clouds at high redshifts have element abundances that are close to primordial. The ratio of deuterium to hydrogen (D/H) within such clouds-which is determined from absorption lines in the spectra of more distant quasars that lie along the same line of sight-provides the best estimate of the density of baryons (omegaB) in the Universe. Previous estimates of D/H in the early Universe have yielded values that differ by about an order of magnitude, with the lower values implying a high density of baryons that may be difficult to reconcile with both estimates of the primordial abundances of other light elements (especially 4He) and the known number of light neutrinos. The accuracy of such D/H determinations is heavily dependent on the inferred column density of neutral hydrogen in the absorbing clouds. Here we report an independent measurement of the neutral hydrogen column density in the cloud towards the quasar Q1937 - 1009, for which one of the low D/H values was derived. Our measurement requires a substantial revision to the D/H value reported previously; we obtain a lower limit of D/H > 4 x 10(-5) for this cloud, which implies omegaB < 0.016 for a Hubble constant of 100 km s(-1) Mpc(-1). This reduced upper limit for the baryon density relieves any conflict with standard Big Bang nucleosynthesis.