The nearest large groups of elliptical galaxies, in the Virgo and Fornax clusters, play a central role in determinations of the Hubble constant, H-0, and hence the cosmological rate of expansion. Because the relative distances between these two clusters and more remote clusters are well known, absolute distance determinations to Virgo and Fornax should establish the Hubble constant for the local Universe. In addition, elliptical galaxies reside predominantly in the cores of clusters, so distance calibrations for ellipticals should minimize the uncertainties due to the possibly large extent of the clusters along the line of sight. A powerful and direct way of establishing such distances is to use the brightest red-giant stars, which have nearly uniform luminosities(1.2). Here we report the direct observation of old red-giant-stars in a dwarf elliptical galaxy in the Virgo cluster. We determine a distance to this galaxy, and thus to the core of the Virgo cluster, of 15.7 +/- 1.5 megaparsecs, from which we estimate a Hubble constant of H-0 = 77 +/- 8 km s(-1) Mpc(-1). Under the assumption of a low-density Universe with the simplest cosmology, the age of the Universe is no more than 12-13 billion years.