We have obtained high resolution \ion Ca2 and \ion Na1 absorption line spectra toward 68 OB stars in the direction of the Vela Supernova Remnant .
The stars lie at distances of 190 – 2800 pc as determined by Hipparcos and spectroscopic parallax estimations .
The presence of high velocity absorption attributable to the remnant along some of the sight lines constrains the remnant distance to 250 \pm 30 pc .
This distance is consistent with several recent investigations that suggest that the canonical remnant distance of 500 pc is too large .