We have constructed Hubble diagrams in B and V for 13 Type Ia supernovae (SNe Ia) found in the course of the Calan/Tololo survey covering an unprecedented range in redshift (0.01 less than Z less than 0.1). As opposed to other published Hubble diagrams, these are solely based on light curves obtained with CCDs, which have been carefully reduced in order to avoid background contamination. Special care was also taken in the extrapolation of peak magnitudes for the SNe that were discovered after maximum light by using five different template light curves representing the range of observed decline rates of SNe Ia. The resulting Hubble diagrams show clear evidence for a distance-dependent dispersion. Although some of the scatter could be due to the peculiar velocities of the host galaxies or to uncorrected dust absorption in the host galaxies, we argue that the dominant source is an intrinsic dispersion in the peak absolute magnitudes of SNe Ia of approximately 0.8 mag in MB and approximately 0.5 mag in MV. If low-luminosity events like SN 1991bg are actually a separate class of supernovae which arise from different progenitors, then the intrinsic dispersion in MB and MV for normal SNe Ia would decrease to approximately 0.3-0.5 mag. This study confirms, in general terms, the finding by Phillips (1993) from a sample of well observed nearby SNe Ia that the absolute B and V magnitudes are correlated with the initial decline rate of the B light curve, although this effect seems to be less pronounced in the Calan/Tololo SNe. Although the number of SNe studied here is relatively small, we find that galaxies having a younger stellar population appear to host the most luminous SNe Ia. We present Hubble diagrams in B and V for the subset of the Calan/Tololo SNe which have decline rates in the range 0.8 less than Delta m15(B) less than 1.5. A dramatic decrease in the scatter in these diagrams is obtained when the data are corrected for the peak luminosity-decline rate relation derived from events in the Phillips sample of nearby SNe Ia covering the same range of decline rates. Using the recently measured Cepheid distance to NGC 5253, a Hubble constant in the range H0 approximately equal to 62-67 km/s/Mpc is calculated when the peak luminosity-decline rate relation is taken into account. The result of ignoring this effect for SN 1972E is to underestimate H0 by approximately 15%.