Cepheid variable stars pulsate in a way that is correlated with their intrinsic luminosity, making them useful as 'standard candles' for determining distances to galaxies; the potential systematic uncertainties in the resulting distances have been estimated to be only 8-10%. They have played a crucial role in establishing the extragalactic distance scale and hence the value of the Hubble constant. Here we report observations of Cepheids in the nearby galaxy NGC4258; the distance calculated from the Cepheids is 8.1 +/- 0.4 Mpc, where the uncertainty does not include possible systematic errors. There is an independently determined geometric distance to this galaxy of 7.2 +/- 0.5 Mpc, based on the observed proper motions of water masers orbiting the central black hole; the distances differ by 1.3sigma. If the maser-based distance is adopted and the Cepheid distance scale revised accordingly, the derived value of the Hubble constant would increase by 12 +/- 9%, while the expansion age of the Universe would decrease by the same amount.