  Large planned photometric surveys will discover hundreds of thousands of
supernovae (SNe), outstripping the resources available for spectroscopic
follow-up and necessitating the development of purely photometric methods to
exploit these events for cosmological study. We present a light-curve fitting
technique for SN Ia photometric redshift (photo-z) estimation in which the
redshift is determined simultaneously with the other fit parameters. We
implement this "LCFIT+Z" technique within the frameworks of the MLCS2k2 and
SALT-II light-curve fit methods and determine the precision on the redshift and
distance modulus. This method is applied to a spectroscopically confirmed
sample of 296 SNe Ia from the SDSS-II Supernova Survey and 37 publicly
available SNe Ia from the Supernova Legacy Survey (SNLS). We have also applied
the method to a large suite of realistic simulated light curves for existing
and planned surveys, including SDSS, SNLS, and LSST. When intrinsic SN color
fluctuations are included, the photo-z precision for the simulation is
consistent with that in the data. Finally, we compare the LCFIT+Z photo-z
precision with previous results using color-based SN photo-z estimates.
