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.
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