The UVOT telescope on the Swift observatory has detected optical afterglow emission from GRB 050319. The flux declines with a power law slope of alpha = -0.57 between the start of observations some 230 seconds after the burst onset (90s after the burst trigger) until it faded below the sensitivity threshold of the instrument after ~5 x 10^4s. There is no evidence for the rapidly declining component in the early light curve that is seen at the same time in the X-ray band. The afterglow is not detected in UVOT shortward of the B-band, suggesting a redshift of about 3.5. The optical V-band emission lies on the extension of the X-ray spectrum, with an optical to X-ray slope of beta = -0.8. The relatively flat decay rate of the burst suggests that the central engine continues to inject energy into the fireball for as long as a few x 10^4s after the burst.