In this study, we present high-resolution millimeter observations of the dust and gas disk of the T Tauri star AS 205 N and its companion, AS 205 S, obtained with the Atacama Large Millimeter Array. The gas disk around AS 205 N, for which infrared emission spectroscopy demonstrates significant deviations from Keplerian motion that has been interpreted as evidence for a disk wind, also displays significant deviations from Keplerian disk emission in the observations presented here. Detections near both AS 205 N and S are obtained in 1.3 mm continuum, 12CO 2-1, 13CO 2-1, and C18O 2-1. The 12CO emission is extended up to ∼2″ from AS 205 N, and both 12CO and 13CO display deviations from Keplerian rotation at all angular scales. Two possible explanations for these observations hold up best to close scrutiny - tidal interaction with AS 205 S or disk winds (or a combination of the two) - and we discuss these possibilities in some detail.