A known physical fact of the anomalous rise of dielectric permittivity ε of C60 fullerite films at ac low frequencies (below 1 kHz) has not had a convincing explanation up to now. Our study was aimed at elucidating the causes of that anomaly. The p-Si/C60/InGa-eutectic structure was made and a frequency dependence of its capacitance was measured. Relying on the experimental result, a versatile analysis of the phenomenon was carried out. It was shown that the anomalous rise of ε value in the low-frequency region resulted from oxygen intercalation of fullerite with formation of C60/O2 molecular groups exhibited significant dipole momenta. The presence of such groups produced a dramatic difference between dielectric permittivity of the crystallites’ surface areas and that of their volumes. As a result, the difference led to an apparent increase in the dielectric permittivity ε of the structure under study.