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 ( 1 Gyr) stars, which are presumed to be dynamically relaxed, and the unrelaxed young ( 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. In the survey region, we classified 60 stars as early-type (23 newly identified) and 74 stars as late-type (61 newly identified). We find that contamination from young stars is significant, with more than twice as many young stars as old stars in our sensitivity range (K' < 15.5) within the central arcsecond. Based on the late-type stars alone, the surface stellar number density profile, SIGMA (R) \propto R-\Gamma, is flat, with \Gamma = -0.27+/-0.19. 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.