Recent experiments have shown that the organic free radical 1,3-bisdiphenylene-2-phenylallyl (BDPA) can induce an Overhauser effect dynamic nuclear polarization in insulating solids, a feat previously considered not to be possible. Here, we establish that this peculiar ability of the BDPA radical stems from its mixed-valence nature and the ensuing intramolecular charge transfer. Using state-of-the-art DMRGSCF calculations, we confirm the class II mixed-valence nature of BDPA with the characteristic double-well potential energy surface, and we investigate the mechanism of the consequent electron hopping. A two-component vibronic Hamiltonian is then employed to compute the rate of electron hopping from a quantum dynamical time-propagation of the density matrix. The predicted hyperfine coupling oscillations indeed fall within the frequency range required for an Overhauser effect. The paradigm of mixed-valence compounds as a mining source opens many possibilities for the development and fine tuning of novel polarizing agents.