  We quantify the effect of supernova Type Ia peculiar velocities on the
derivation of cosmological parameters. The published distant and local Ia SNe
used for the Supernova Legacy Survey first-year cosmology report form the
sample for this study. While previous work has assumed that the local SNe are
at rest in the CMB frame (the No Flow assumption), we test this assumption by
applying peculiar velocity corrections to the local SNe using three different
flow models. The models are based on the IRAS PSCz galaxy redshift survey, have
varying beta = Omega_m^0.6/b, and reproduce the Local Group motion in the CMB
frame. These datasets are then fit for w, Omega_m, and Omega_Lambda using
flatness or LambdaCDM and a BAO prior. The chi^2 statistic is used to examine
the effect of the velocity corrections on the quality of the fits. The most
favored model is the beta=0.5 model, which produces a fit significantly better
than the No Flow assumption, consistent with previous peculiar velocity
studies. By comparing the No Flow assumption with the favored models we derive
the largest potential systematic error in w caused by ignoring peculiar
velocities to be Delta w = +0.04. For Omega_Lambda, the potential error is
Delta Omega_Lambda = -0.04 and for Omega_m, the potential error is Delta
Omega_m < +0.01. The favored flow model (beta=0.5) produces the following
cosmological parameters: w = -1.08 (+0.09,-0.08), Omega_m = 0.27 (+0.02,-0.02)
assuming a flat cosmology, and Omega_Lambda = 0.80 (+0.08,-0.07) and Omega_m =
0.27 (+0.02,-0.02) for a w = -1 (LambdaCDM) cosmology.
