Using first-principles calculations, we show that a specific chemical ordering of Na and Bi in Na0.5Bi0.5TiO3 is responsible for the co-existence of its ferroelectric phases with rhombohedral R3c and monoclinic Cc structures, which are relevant to its morphotropic phase boundary and large piezoelectric response. We identify the signatures of chemical ordering in the calculated phonon spectra and establish the prevalence of A-type ordering through comparison with experiment. We uncover a mechanism of the observed electric field induced Cc to lower energy R3c structural transformation promoted by a hybrid soft mode involving a combination of TiO6 rotations and a polar component. © 2016 AIP Publishing LLC.