We present new high-resolution (similar to 0.09) H-band imaging observations of the circumstellar disk around the T Tauri star SU Aur. Our observations with Subaru-HiCIAO have revealed the presence of scattered light as close as 0.15 (similar to 20 AU) to the star. Within our image, we identify bright emission associated with a disk with a minimum radius of similar to 90 AU, an inclination of similar to 35 degrees from the plane of the sky, and an approximate PA of 15 degrees for the major axis. We find a brightness asymmetry between the northern and southern sides of the disk due to a non-axisymmetric disk structure. We also identify a pair of asymmetric tail structures extending east and west from the disk. The western tail extends at least 2.5 (350 AU) from the star, and is probably associated with a reflection nebula previously observed at optical and near-IR wavelengths. The eastern tail extends at least 1. (140 AU) at the present signal-to-noise. These tails are likely due to an encounter with an unseen brown dwarf, but our results do not exclude the explanation that these tails are outflow cavities or jets.