In search of stellar occultation candidates, the Flagstaff Automatic Scanning Transit Telescope (FASTT) was used to scan the sky through which the Centaur 5145 Pholus will pass during the period 1999-2005. Positions for 98,602 stars (7.0<V<17.7) were determined using differential reductions and the ACT catalog of star positions and proper motions, and accuracies of ±20 mas in each coordinate were achieved, except for the faintest stars observed. During the period of our search, Pholus passes within 1".5 of 100 of these stars, which have been identified as occultation candidates in this paper. Circumstances for the possible occultations are given, including finder charts for the 15 brightest stars. Since the radius of Pholus subtends approximately 10 mas, considerable astrometric effort will be required near the time of a potential event to determine whether it will result in an observable occultation. A stellar occultation observed from multiple sites can be used to determine the precise radius and albedo for this object.