Helicity and alpha effect driven by the nonaxisymmetric Tayler instability of toroidal magnetic fields in stellar radiation zones are computed. In the linear approximation a purely toroidal field always excites pairs of modes with identical growth rates but with opposite helicity so that the net helicity vanishes. If the magnetic background field has a helical structure by an extra (weak) poloidal component then one of the modes dominates producing a net kinetic helicity anticorrelated to the current helicity of the background field. The mean electromotive force is computed with the result that the alpha effect by the most rapidly growing mode has the same sign as the current helicity of the background field. The alpha effect is found as too small to drive an alpha^{2} dynamo but the excitation conditions for an alphaOmega dynamo can be fulfilled for weak poloidal fields. Moreover, if the dynamo produces its own alpha effect by the magnetic instability then problems with its sign do not arise. For all cases, however, the alpha effect shows an extremely strong concentration to the poles so that a possible alphaOmega dynamo might only work at the polar regions. Hence, the results of our linear theory lead to a new topological problem for the existence of large-scale dynamos in stellar radiation zones on the basis of the current-driven instability of toroidal fields.
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