The efficiency of an organic light-emitting diode (OLED) depends on the microscopic orientation of transition dipole moments of the molecular emitters. The most effective materials used for light generation have 3-fold symmetry, which prohibits a priori determination of dipole orientation due to the degeneracy of the fundamental transition. Single-molecule spectroscopy reveals that the model triplet emitter tris(1-phenylisoquinoline)iridium(III) (Ir(piq)3) does not behave as a linear dipole, radiating with lower polarization anisotropy than expected. Spontaneous symmetry breaking occurs in the excited state, leading to a random selection of one of the three ligands to form a charge-transfer state with the metal. This nondeterministic localization is revealed in switching of the degree of linear polarization of phosphorescence. Polarization scrambling likely raises out-coupling efficiency and should be taken into account when deriving molecular orientation of the guest emitter within the OLED host from ensemble angular emission profiles.