We discuss the possibility that a solution of the strong CP problem via the introduction of a chiral U(1), à la Peccei-Quinn, may also provide a natural scenario for explaining the apparent depletion of the solar neutrino flux through matter enhanced neutrino oscillations. The smallness of the neutrino masses is related to the scale at which the U(1)PQ symmetry is spontaneously broken, without introducing right-handed neutrino fields and invoking the see-saw mechanism. The model is consistent with all present experimental results. In particular, the phenomenology associated to the presence of an “invisible” axion is the same as in the Dine-Fischler-Srednicki-Zhitnisky model with the exception of a very small coupling to neutrinos.