The Supernova Cosmology Project has discovered over twenty-eight supernovae (SNe) at 0.35 <z < 0.65 in an ongoing program that uses Type Ia SNe as high-redshift distance indicators. Here we present measurements of the ratio between the locally observed and global Hubble constants, H_0^L/H_0^G, based on the first 7 SNe of this high-redshift data set compared with 18 SNe at z <= 0.1 from the Calan/Tololo survey. If Omega_M <= 1, then light-curve-width corrected SN magnitudes yield H_0^L/H_0^G < 1.10 (95% confidence level) in both a Lambda=0 and a flat universe. The analysis using the SNe Ia as standard candles without a light-curve-width correction yields similar results. These results rule out the hypothesis that the discrepant ages of the Universe derived from globular clusters and recent measurements of the Hubble constant are attributable to a locally underdense bubble. Using the Cepheid-distance-calibrated absolute magnitudes for SNe Ia of Sandage (1996}, we can also measure the global Hubble constant, H_0^G. If Omega_M >= 0.2, we find that H_0^G < 70 km/s/Mpc in a Lambda=0 universe and H_0^G < 78 km/s/Mpc in a flat universe, correcting the distant and local SN apparent magnitudes for light curve width. Lower results for H_0^G are obtained if the magnitudes are not width corrected. Comment: 13 pages, 2 Postscript figures. Preprint also available at http://www-supernova.lbl.gov . To appear in ApJ Letters