Lead dioxide has been used for over a century in the lead-acid battery. Many fundamental questions concerning PbO(2) remain unanswered, principally: (i) is the bulk material a metal or a semiconductor, and (ii) what is the source of the high levels of conductivity? We calculate the electronic structure and defect physics of PbO(2), using a hybrid density functional, and show that it is an n-type semiconductor with a small indirect band gap of similar to 0.2 eV. The origin of electron carriers in the undoped material is found to be oxygen vacancies, which forms a donor state resonant in the conduction band. A dipole-forbidden band gap combined with a large carrier induced Moss-Burstein shift results in a large effective optical band gap. The model is supported by neutron diffraction, which reveals that the oxygen sublattice is only 98.4% occupied, thus confirming oxygen substoichiometry as the electron source.