Both galaxy distances and velocities are required for the determination of the expansion rate of the Universe, as described by the Hubble constant H-0. The radial velocities of galaxies arise not just from this expansion but also from random components and large-scale flows. To reach out to distances dominated by the overall cosmic expansion, it is necessary to probe large physical scales where galaxy-galaxy and galaxy-cluster interactions become less important. But accurate distances of nearby galaxies and clusters (commonly measured(1) using Cepheid variable stars) are nevertheless required to calibrate the indirect distance indicators generally used to measure these large scales. Here we report a Cepheid distance of 18.6 +/- 1.9 (statistical error) +/- 1.9 Mpe (systematic error) for the galaxy NGC1365 in Fornax, a cluster of galaxies in the Southern Hemisphere. We find a value of H-0 = 70 km s(-1) Mpc(-1) from Fornax alone, and 73 km s(-1) Mpc.(-1) from the intervening galaxy flow, each corrected for infall into the Virgo cluster. These values are consistent with the Hubble constant measured in the far field using secondary methods(2). Our data support previous suggestions(3-5) that the local small-scale velocity field has very small scatter (similar to+/-70km s(-1)).