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A careful assessment of current uncertainties in stellar physics (opacities, nuclear reaction rates, equation of state effects, diffusion, rotation, and mass loss), in the chemistry of globular cluster (GC) stars, and in the cluster distance scale, suggests that the most metal-poor (presumably the oldest) of the Galaxy's GCs have ages near 15 Gyr. Ages below 12 Gyr or above 20 Gyr appear to be highly unlikely. If these approx. 2 σ limits are increased by ∼ 1 Gyr to account for the formation time of the globulars, and if standard Friedmann cosmologies with the cosmological constant set to zero are assumed, then the GC constraint on the present age of the Universe (t0 ≥ 13 Gyr) implies that the Hubble constant H0 ≤ 51 km s[sup -1] Mpc[sup -1] if the density parameter Ω = 1 or ≤ 62 km s[sup -1] Mpc[sup -1] if Ω = 0.3. [ABSTRACT FROM AUTHOR]