We report the first observation of a field-dependent mass in a hybridizing f-electron system. CeB6 is an ordered moment heavy fermion system with an electronic specific heat coefficient γ of order 225-300 mJ/mole K2. Using the de Haas-van Alphen effect at temperatures as low as 60 mK in steady magnetic fields as large as 22 T, we observe a cyclotron orbit of frequency 8680 T for fields along the [100] direction. The mass of this orbit was measured at eight fixed fields and found to decrease from 18me to 8me as the field increases from 12 to 22 T. The observed Fermi surface is very similar to that of LaB6, indicating that the f-electrons are largely local rather than itinerant in CeB6, a picture confirmed by bandstructure calculations. The observed field dependence of the cyclotron mass is consistent with the low-energy scale of the system as measured, for example, by the Kondo temperature. Our results are compared with Fermi surface observations in other heavy fermion systems.