  We use a sample of 121 spectroscopically normal Type Ia supernovae (SNe Ia)
to show that their intrinsic color is correlated with their ejecta velocity, as
measured from the blueshift of the Si II 6355 feature near maximum brightness,
v_Si. The SN Ia sample was originally used by Wang et al. (2009) to show that
the relationship between color excess and peak magnitude, which in the absence
of intrinsic color differences describes a reddening law, was different for two
subsamples split by v_Si (defined as "Normal" and "High-Velocity"). We verify
this result, but find that the two subsamples have the same reddening law when
extremely reddened events (E(B-V) > 0.35 mag) are excluded. We also show that
(1) the High-Velocity subsample is offset by ~0.06 mag to the red from the
Normal subsample in the (B_max - V_max) - M_V plane, (2) the B_max - V_max
cumulative distribution functions of the two subsamples have nearly identical
shapes, but the High-Velocity subsample is offset by ~0.07 mag to the red in
B_max - V_max, and (3) the bluest High-Velocity SNe Ia are ~0.10 mag redder
than the bluest Normal SNe Ia. Together, this evidence indicates a difference
in intrinsic color for the subsamples. Accounting for this intrinsic color
difference reduces the scatter in Hubble residuals from 0.190 mag to 0.130 mag
for SNe Ia with A_V < 0.7 mag. The scatter can be further reduced to 0.109 mag
by exclusively using SNe Ia from the Normal subsample. Additionally, this
result can at least partially explain the anomalously low values of R_V found
in large SN Ia samples. We explain the correlation between ejecta velocity and
color as increased line blanketing in the High-Velocity SNe Ia, causing them to
become redder. We discuss some implications of this result, and stress the
importance of spectroscopy for future SN Ia cosmology surveys, with particular
focus on the design of WFIRST.
