  We study spontaneous breakdown of chiral symmetry during the nonlinear
evolution of the Tayler instability. We start with an initial steady state of
zero helicity. Within linearized perturbation calculations, helical
perturbations of this initial state have the same growth rate for either sign
of helicity. Direct numerical simulations (DNS) of the fully nonlinear
equations, however, show that an infinitesimal excess of one sign of helicity
in the initial perturbation gives rise to a saturated helical state. We further
show that this symmetry breaking can be described by weakly nonlinear
finite--amplitude equations with undetermined coefficients which can be deduced
solely from symmetry consideration. By fitting solutions of the amplitude
equations to data from DNS we further determine the coefficients of the
amplitude equations.
