B-band light-curve rise times for eight unusually well-observed nearby Type Ia supernovae (SNe) are fitted by a newly developed template-building algorithm, using light-curve functions that are smooth, flexible, and free of potential bias from externally derived templates and other prior assumptions. From the available literature, photometric BVRI data collected over many months, including the earliest points, are reconciled, combined, and fitted to a unique time of explosion for each SN. On

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... rage, after they are corrected for light-curve decline rate, three SNe rise in 18.81 +- 0.36 days, while five SNe rise in 16.64 +- 0.21 days. If all eight SNe are sampled from a single parent population (a hypothesis not favored by statistical tests), the rms intrinsic scatter of the decline-rate-corrected SN rise time is 0.96 +0.52 -0.25 days -- a first measurement of this dispersion. The corresponding global mean rise time is 17.44 +- 0.39 days, where the uncertainty is dominated by intrinsic variance. This value is ~2 days shorter than two published averages that nominally are twice as precise, though also based on small samples. When comparing high-z to low-z SN luminosities for determining cosmological parameters, bias can be introduced by use of a light-curve template with an unrealistic rise time. If the period over which light curves are sampled depends on z in a manner typical of current search and measurement strategies, a two-day discrepancy in template rise time can bias the luminosity comparison by ~0.03 magnitudes.