Two independent sets of Chandra and HST images of the nuclear region of M31 allow registration of X-ray and optical images to similar to 0."1. This registration shows that none of the bright (similar to 10(37) ergs s(-1)) X- ray sources near the nucleus is coincident with the central supermassive black hole, M31*. A 50 ks Chandra HRC image shows 2.5 sigma evidence for a faint (similar to 10(36) ergs s(-1)) discrete source that is consistent with the position of M31*. The Bondi radius of M31* is 0."9, making it one of the few supermassive black holes with a resolvable accretion flow. This large radius and the previous detections of diffuse X- ray-emitting gas in the nuclear region make M31* one of the most secure cases for a radiatively inefficient accretion flow and place some of the most severe constraints on the radiative processes in such a flow.