  We describe images of the center of the dense globular cluster M15 (NGC 7078)
obtained with the Hubble Space Telescope Wide Field and Planetary Camera 2
(WFPC2). Data taken in the F336W, F439W, and F555W filters (approximately U, B,
and V) are used to study the surface density distribution of the
$\sim3\times10^4$~stars detected in a 5~arcmin$^2$ region within $r<2'$
(6.7$\,$pc) of the cluster center. The surface density of stars in M15 (after
correction for the effects of incompleteness and photometric bias/scatter) is
well represented by a power law in radius: $N(r)\sim{r}^{-0.82\pm0.12}$, over
the radial range $0.3''$ (0.017$\,$pc) to $6''$. The observed power law is
remarkably similar to what is expected if the center of the cluster harbors a
massive black hole. Non-parametric estimates of the density profile show a
monotonic rise with decreasing radius all the way in to $r=0.3''$, the smallest
radius at which the density can be reliably measured; there is no indication
that the profile flattens at smaller radii. Any flat core of radius larger than
$2''$ (0.11$\,$pc) in the stellar distribution is ruled out at the $>95$\%
significance level. The star count profile is consistent with that expected
from core-collapse models or with the predicted distribution around a massive
(few times $10^3\,M_\odot$) black hole. The close triplet of bright stars,
AC~214, is within $0.5''$ ($1.5\sigma$) of the cluster centroid position.
