The ability to characterize gust-induced aeroelastic behavior of lifting surfaces is critical for improving the prediction of unsteady loads and for developing reliable analytical and numerical frameworks, particularly under strongly nonlinear flow conditions. An experimental investigation is conducted in a low-speed wind tunnel to examine the interaction between prescribed transverse gusts and an elastically mounted NACA 64-418 airfoil with a single torsional degree of freedom. A sequence of four discrete gusts is shown to progressively amplify the wing response and ultimately induce a self-sustained limit cycle oscillation. Analysis of the gust encounters reveals a phase lag between the aerodynamic pitching moment and the structural response, allowing positive aerodynamic work input during the pitch-up phase of the airfoil. Once established, the limit cycle oscillation occurs at a frequency close to the natural torsional frequency of the system and exhibits pronounced aerodynamic hysteresis. Phase-averaged aerodynamic loads and pressure measurements indicate that the flow remains largely separated over most of the upper surface during the oscillation. The results provide experimental insight into the mechanisms of gust-induced stall flutter and offer an accurate dataset for the validation of numerical aeroelastic models.