Accurate distances to galaxies are critical for determining the present expansion rate of the Universe or Hubble constant (H-o). An important step in resolving the current uncertainty in H-o is the measurement of the distance to the Virgo cluster of galaxies. New observations using the Hubble Space Telescope yield a distance of 17.1 +/- 1.8 Mpc to the Virgo cluster galaxy M100. This distance leads to a value of H-o = 80 +/- 17 km s(-1) Mpc(-1). A comparable value of H-o is also derived from the Coma cluster using independent estimates of its distance ratio relative to the Virgo cluster.