When Comet Hale-Bopp was first discovered at a heliocentric distance of ~7.2 AU, its activity appeared to be controlled by the outgassing of the highly volatile CO molecule. Its gas production remained CO-driven until about 4 AU when the outgassing became controlled by the less volatile H2O molecule. While the outgassing around this distance is consistent with the sublimation from a large ``dirty snowball'' composed dominantly of H2O, the subsequent outgassing at smaller heliocentric distance up to perihelion (d ~ 0.914 AU) falls consistently below the predictions of such a model. In this paper, we use the earliest chemical differentiation model of the cometary nucleus developed by Houpis et al., with a few modifications, to show that the continuous chemical differentiation of a deepening layer of the cometary nucleus which has made multiple passages into the inner solar system can explain comet Hale-Bopp's observed pre-perihelion production rate curve. It also predicts a hysteresis with the gas production rate profiles falling systematically lower post-perihelion. The model suggests that comet Hale-Bopp is a complex combination of dust, clathrate, and volatile (mainly CO), the gas production of which changes from being CO-driven to H2O driven around 4 AU. Furthermore, the thermal insulation provided by a growing dust mantle inside ~3.5 AU causes the H2O production rate curve to flatten-out.