  The transversity Generalized Parton Distributions (tGPDs) and related
transversity form factors of the pion are evaluated in chiral quark models,
both local (Nambu--Jona-Lasinio) and nonlocal, involving a momentum-dependent
quark mass. The obtained tGPDs satisfy all a priori formal requirements, such
as the proper support, normalization, and polynomiality. We evaluate
generalized transversity form factors accessible from the recent lattice QCD
calculations. These form factors, after the necessary QCD evolution, agree very
well with the lattice data, confirming the fact that the spontaneously broken
chiral symmetry governs the structure of the pion also in the case of the
transversity observables.
