  We report on the structure of the nuclear star cluster in the innermost 0.16
pc of the Galaxy as measured by the number density profile of late-type giants.
Using laser guide star adaptive optics in conjunction with the integral field
spectrograph, OSIRIS, at the Keck II telescope, we are able to differentiate
between the older, late-type ($\sim$ 1 Gyr) stars, which are presumed to be
dynamically relaxed, and the unrelaxed young ($\sim$ 6 Myr) population. This
distinction is crucial for testing models of stellar cusp formation in the
vicinity of a black hole, as the models assume that the cusp stars are in
dynamical equilibrium in the black hole potential. Based on the late-type stars
alone, the surface stellar number density profile, $\Sigma(R) \propto
R^{-\Gamma}$, is flat, with $\Gamma = -0.27\pm0.19$. Monte Carlo simulations of
the possible de-projected volume density profile, n(r) $\propto r^{-\gamma}$,
show that $\gamma$ is less than 1.0 at the 99.73 % confidence level. These
results are consistent with the nuclear star cluster having no cusp, with a
core profile that is significantly flatter than predicted by most cusp
formation theories, and even allows for the presence of a central hole in the
stellar distribution. Of the possible dynamical interactions that can lead to
the depletion of the red giants observable in this survey -- stellar
collisions, mass segregation from stellar remnants, or a recent merger event --
mass segregation is the only one that can be ruled out as the dominant
depletion mechanism. The lack of a stellar cusp around a supermassive black
hole would have important implications for black hole growth models and
inferences on the presence of a black hole based upon stellar distributions.
