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Chirped Lommel Gaussian vortex beams (LGVBs) propagating in strongly nonlocal nonlinear fractional Schrödinger equation (NFSE) are numerically studied for the first time. We verify that the chirped LGVBs perform autofocusing effects periodically. The propagation trajectory, the focal position and the focal intensity of the chirped LGVBs are deeply influenced by the appropriate selection of the parameters of the initial beams as well as the Lévy index of fractional diffraction effect in the strongly nonlocal NFSE. Moreover, the Poynting vector and the angular momentum of the beams are also researched. The findings demonstrate many interesting properties related to the chirped LGVBs propagating in the strongly nonlocal nonlinear fractional NFSE, which can broaden the research field of the chirped LGVBs.