  We obtained U_330 and B band images of the M31 nucleus using the High
Resolution Camera of the Advanced Camera for Surveys on board the Hubble Space
Telescope (HST). The spatial resolution in the U_330-band, 0.03" FWHM, or 0.1
pc at M31, is sufficient to resolve the outskirts of the compact cluster (P3)
of UV-bright stars surrounding the M31 black hole. The center of the cluster is
marked by an extended source that is both brighter and redder than the other
point sources within P3; it is likely to be a blend of several bright stars. We
hypothesize that it marks the location of the M31 black hole. Both stellar
photometry and a surface brightness fluctuation analysis, show that the P3
stellar population is consistent with early-type main sequence stars formed in
a ~100 - ~200 Myr old starburst population. Evolutionary tracks of post early
asymptotic giant-branch stars, associated with late-stage evolution of an old
population, also traverse the U and U-B domain occupied by the P3 stars; but we
argue that only a few stars could be accounted for that way. PEAGB evolution is
very rapid, and there is no progenitor population of red giants associated with
P3. The result that P3 comprises young stars is consistent with inferences from
earlier HST observations of the integrated light of the cluster. Like the Milky
Way, M31 harbors a black hole closely surrounded by apparently young stars.

Cosmology and Nongalactic Astrophysics