  We introduce a method for identifying "twin" Type Ia supernovae, and using
them to improve distance measurements. This novel approach to Type Ia supernova
standardization is made possible by spectrophotometric time series observations
from the Nearby Supernova Factory (SNfactory). We begin with a well-measured
set of supernovae, find pairs whose spectra match well across the entire
optical window, and then test whether this leads to a smaller dispersion in
their absolute brightnesses. This analysis is completed in a blinded fashion,
ensuring that decisions made in implementing the method do not inadvertently
bias the result. We find that pairs of supernovae with more closely matched
spectra indeed have reduced brightness dispersion. We are able to standardize
this initial set of SNfactory supernovae to 0.083 +/- 0.012 magnitudes,
implying a dispersion of 0.072 +/- 0.010 magnitudes in the absence of peculiar
velocities. We estimate that with larger numbers of comparison SNe, e.g, using
the final SNfactory spectrophotometric dataset as a reference, this method will
be capable of standardizing high-redshift supernovae to within 0.06-0.07
magnitudes. These results imply that at least 3/4 of the variance in Hubble
residuals in current supernova cosmology analyses is due to previously
unaccounted-for astrophysical differences among the supernovae
