The central stellar bulge of our Galaxy is commonly held to consist predominantly of a coeval population of very old (~ 10^10 yr) stars^1-3. On the other hand, evidence for both very young^4 and intermediate-age stars^5,6 in the bulge is accumulating. Here we argue that star formation has been occurring in the molecular gas near the center of the bulge throughout the lifetime of the Galaxy, and that the resulting stellar population is evident as the prominent infrared^7,8 ``r^-2 central star cluster'' (a cluster whose space density decreases as the square of the distance from the center). Although our hypothesis is at odds with the standard view that this central cluster is the innermost part of the more extended and ancient bulge^9-11, sustained star formation is consistent with both the available observational data, and simple models of mass inflow and collisionally induced star formation in this region. Even if the central star-formation rate is relatively modest, it appears that the stellar population of the Galactic bulge has been augmented substantially since its birth.