Emission from atomic hydrogen at a wavelength of 21 centimetres had been observed from galaxies at a maximum redshift of 0.4, but is now reported at a redshift of about 1. Baryonic processes in galaxy evolution include the infall of gas onto galaxies to form neutral atomic hydrogen, which is then converted to the molecular state (H-2), and, finally, the conversion of H(2)to stars. Understanding galaxy evolution thus requires an understanding of the evolution of stars and of neutral atomic and molecular hydrogen. For the stars, the cosmic star-formation rate density is known to peak at redshifts from 1 to 3, and to decline by an order of magnitude over approximately the subsequent 10 billion years(1); the causes of this decline are not known. For the gas, the weakness of the hyperfine transition of H iat 21-centimetre wavelength-the main tracer of the H icontent of galaxies-means that it has not hitherto been possible to measure the atomic gas mass of galaxies at redshifts higher than about 0.4; this is a critical gap in our understanding of galaxy evolution. Here we report a measurement of the average H imass of star-forming galaxies at a redshift of about one, obtained by stacking(2)their individual H i21-centimetre emission signals. We obtain an average H imass similar to the average stellar mass of the sample. We also estimate the average star-formation rate of the same galaxies from the 1.4-gigahertz radio continuum, and find that the H imass can fuel the observed star-formation rates for only 1 to 2 billion years in the absence of fresh gas infall. This suggests that gas accretion onto galaxies at redshifts of less than one may have been insufficient to sustain high star-formation rates in star-forming galaxies. This is likely to be the cause of the decline in the cosmic star-formation rate density at redshifts below one.