Accurate distances to galaxies are critical to determining the present expansion rate of the Universe or Hubble Constant (H<sub>0</sub>). An important step in resolving the current uncertainty in H<sub>0</sub> 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<sub>0</sub> = 17 km/sec/Mpc. A comparable value of H<sub>0</sub> is also derived from the Coma cluster using independent estimates of its distance ratio relative to the Virgo cluster.