Polysilylenes, organic polymers with silicon backbone, represent a new class of dielectric materials capable of transporting injected holes. Charge transport in poly(methylphenylsilylene), a typical representative of these polymers, is thermally activated and relatively non-dispersive over a wide range of temperatures. The carrier drift mobility is high for organic glasses, near 10-4 cm2N.s. at E = 105 V/cm, and field dependent at T < Tg. The charge transport in polysilylenes has most of the characteristics of hopping transport among discrete states, but it is insensitive to the nature of the side groups (aromatic or aliphatic) and the molecular weight of the polymer. The proposed mechanism of transport is that of hopping among rather short segments of the silicon chain.