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 (H2), and, finally, the conversion of H2 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 years1; the causes of this decline are not known. For the gas, the weakness of the hyperfine transition of H I at 21-centimetre wavelength-the main tracer of the H I content 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 I mass of star-forming galaxies at a redshift of about one, obtained by stacking2 their individual H I 21-centimetre emission signals. We obtain an average H I mass 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 I mass 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.