This paper reports the experimental demonstration of time-dependent dielectric breakdown in GaN-based high-electron mobility transistors (HEMTs) submitted to OFF-state stress. Based on combined breakdown measurements, constant voltage stress tests, and 2-D simulations, we demonstrate the following relevant results. First, GaN-based HEMTs with a breakdown voltage higher than 1000 V (evaluated by dc measurements) may show time-dependent failure when exposed to OFF-state stress with VDS in the range 600-700 V. Second, time-to-failure (TTF) is Weibull-distributed, and has an exponential dependence on the stress voltage level. Third, time-dependent breakdown is ascribed to the failure of the SiN dielectric at the edge of the gate overhang, on the drain side. Fourth, 2-D simulations confirm that-in this region-the electric field exceeds 6 MV/cm, i.e., the dielectric strength of SiN. Finally, we demonstrate that by limiting the electric field in the nitride through epitaxy and process improvements, it is possible to increase the TTF by three orders of magnitude.