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We calculate the rate of collisional decay of the axial charge in an ultrarelativistic electron-positron plasma, also known as the chirality flipping rate. We find that contrary to the existing estimates, the chirality flipping rate appears already in the first order in the fine-structure constant α and is therefore orders of magnitude greater than previously believed. The main channels for the rapid relaxation of the axial charge are the collinear emission of a weakly damped photon and the Compton scattering. The latter contributes to the O(α) result because of the infrared divergence in its cross section, which is regularized on the soft scale ∼eT due to the thermal corrections. Our results are important for the description of the early Universe processes (such as leptogenesis or magnetogenesis) that affect differently left- and right-chiral fermions of the Standard Model, as discussed in more details in the companion Letter. [ABSTRACT FROM AUTHOR]