We assume that QCD can be described in a certain kinematical regime by an effective string theory. This hadronic string must couple to background chiral fields in a chirally invariant manner, taking into account the true chirally non-invariant QCD vacuum. By requiring conformal symmetry of the string and the unitarity constraint on chiral fields we reconstruct the equations of motion for the latter ones. These provide a consistent background for the propagation of the string. By further requiring locality of the effective action we recover the Lagrangian of non-linear sigma model of pion interactions. The prediction is totally unambiguous and parameter-free. The estimated chiral structural constants of Gasser and Leutwyler fit very well the phenomenological values.