  We present an empirical method which uses visual band light curve shapes
(LCS) to estimate the luminosity of type Ia supernovae (SN Ia). This method is
first applied to a ``training set'' of 8 SN Ia light curves with independent
distance estimates to derive the correlation between the LCS and the
luminosity. We employ a linear estimation algorithm of the type developed by
Rybicki and Press (1992). The result is similar to that obtained by Hamuy et
al. (1995a) with the advantage that LCS produces quantitative error estimates
for the distance. We then examine the light curves for 13 SN Ia to determine
the LCS distances of these supernovae. The Hubble diagram constructed using
these LCS distances has a remarkably small dispersion of $\sigma_V$ = 0.21 mag.
We use the light curve of SN 1972E and the Cepheid distance to NGC 5253 to
derive $67 \pm 7 $ km s$^{-1}$ Mpc$^{-1}$ for the Hubble constant.
