We present high spatial resolution maps of ro-vibrational molecular hydrogen emission from the environment of the GG Tau A binary component in the GG Tau quadruple system . The H _ { 2 } v = 1-0 S ( 1 ) emission is spatially resolved and encompasses the inner binary , with emission detected at locations that should be dynamically cleared on several hundred-year timescales . Extensions of H _ { 2 } gas emission are seen to \sim 100 AU distances from the central stars . The v = 2-1 S ( 1 ) emission at 2.24 \mu m is also detected at \sim 30 AU from the central stars , with a line ratio of 0.05 \pm 0.01 with respect to the v = 1-0 S ( 1 ) emission . Assuming gas in LTE , this ratio corresponds to an emission environment at \sim 1700 K . We estimate that this temperature is too high for quiescent gas heated by X-ray or UV emission from the central stars . Surprisingly , we find that the brightest region of H _ { 2 } emission arises from a spatial location that is exactly coincident with a recently revealed dust “ streamer ” which seems to be transferring material from the outer circumbinary ring around GG Tau A into the inner region . As a result , we identify a new excitation mechanism for ro-vibrational H _ { 2 } stimulation in the environment of young stars . The H _ { 2 } in the GG Tau A system appears to be stimulated by mass accretion infall as material in the circumbinary ring accretes onto the system to replenish the inner circumstellar disks . We postulate that H _ { 2 } stimulated by accretion infall could be present in other systems , particularly binaries and “ transition disk ” systems which have dust cleared gaps in their circumstellar environments .