The one-electron states responsible for hole transport in the high-mobility semicrystalline polymer PBTTT are investigated using a combination of large-scale electronic structure calculations (with the DFTB method) and classical molecular dynamics simulations. The validity of the structural model is established by comparison with the available data from crystallography, including the paracrystallinity parameter. The localization characteristics of the states at the edge of the valence band, their geometry, and their time evolution clearly indicate the characteristics of PBTTT that are at the origin of its improved mobility: i) the orbitals become very rapidly delocalized within few tens of eV from the valence band edge, that is, the density of trap states is low and the mobility edge is very close to the valence band edge; ii) a very large delocalization of states across chains is observed; iii) the traps, determined by local distortions of the chain, have a typical lifetime of less than 0.1 ns, that is, the conformational changes of the polymer due to its thermal fluctuations are sufficient to induce a detrapping of the charge carrier and the traps are self-healing.