Our previous experiments on the dynamics of premixed flames on circular porous plug burners have demonstrated a variety of periodic pulsating flames with different spatial and temporal characteristics. In the radial mode the circular flame front expands and contracts, periodically changing its radial extent. As the system parameters are adjusted near the extinction boundary, a sequence of transitions is observed. First, the radial mode loses its circular symmetry but remains periodic. Next, it undergoes a transition to a chaotic state. Finally, it makes a transition to extinction. All periodic pulsating modes are separated from the extinction boundary by a region of chaotic dynamics. The characteristics of chaotic flame dynamics beyond the extinction limit are discussed. The spatial and temporal characteristics of this chaotic mode are discussed and compared with the relevant theoretical studies.