The Hubble Space Telescope is breaking a long-standing impasse in phys
ical cosmology. The distances of galaxies sufficiently remote for thei
r random velocities to be negligible can now be measured in two steps,
the first using Cepheid variable stars as standard candles to approxi
mately 20 Mpc, the second using a variety of secondary distance indica
tors to distances 10 times larger. The present key project on the Hubb
le Constant aims to measure H-0 to 10%. Current results with approxima
tely 20% uncertainty suggest that cosmologists will be offered a dilem
ma: an open Universe or a vacuum energy dominated Universe.