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 \leq 0.1 from the Calán/Tololo survey . If \Omega _ { M } \leq 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 et al . ( 1996 ) ] , we can also measure the global Hubble constant , H _ { 0 } ^ { G } . If \Omega _ { M } \geq 0.2 , we find that H _ { 0 } ^ { G } < 70 { ~ { } km~ { } s ^ { -1 } ~ { } Mpc ^ { -1 } } in a \Lambda = 0 universe and H _ { 0 } ^ { G } < 78 { ~ { } km~ { } s ^ { -1 } ~ { } Mpc ^ { -1 } } 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 .