We present Hubble Space Telescope (HST) Near-Infrared Camera and Multiobject Spectrometer (NICMOS) observations as evidence that continuous star formation has created much of the central stellar cusp of the Galaxy. The data are the deepest ever obtained for a Galactic Center (GC) population, being >50% complete for \mnk<19.3, or initial stellar masses > 2 \Msun. We use Geneva and Padova stellar evolution models to produce synthetic luminosity functions for burst and continuous star formation scenarios, finding that the observations are fit best by continuous star formation at a rate that is consistent with the recent star formation activity that produced the three massive young clusters in the central 50 \pc. Further, it is not possible to fit the observations with ancient burst models, such as would be appropriate for an old population like that in Baade's Window or NGC6528.