The realization of large powerful all-solid-state batteries is still hampered by the availability of environmentally friendly and low-cost Li ion conductors that can easily be produced on a large scale and with high reproducibility. Advanced solid electrolytes benefit from fast ion-selective transport and non-flammability, but they may have low electrochemical stability with respect to Li metal. Sol-gel-synthesized lithium titanium aluminum phosphate Li(1.5)Al(0.5)Ti(1.5)(PO4)3 (LATP), which was prepared via a new synthesis route taking advantage of an annealing step at relatively low temperatures, has the potential to become one of the major players in this field although it may suffer from reduction upon direct contact with metallic lithium. Its ion dynamics is, however, as yet poorly understood. In the present study, (7)Li nuclear magnetic resonance (NMR) spectroscopy was used to monitor the key Li jump processes on the atomic scale. NMR relaxation clearly reveals heterogeneous dynamics comprising distinct ultra-fast and slower diffusion processes. The high Li ion self-diffusion coefficients deduced originate from a rapid Li exchange with activation energies as low as 0.16 eV which means that sol-gel synthesized LATP is superior to other solid electrolytes. Our NMR results fully support recent theoretical investigations on the underlying diffusion mechanism, indicating that to rapidly jump from site to site, the ions use interstitial sites connected by low-energy barriers in LATP.