Bullseye Sharp Shooter Rubber Band Pistol
From the National Firearms Museum:
Patented by Dr. Claude Bunten, a dentist in Wyoming, the Bulls-Eye Sharp Shooter rubber band pistol was a popular toy gun that was invented in the late 1920s. A .177 caliber BB was propelled by a rubber band in the gun that was designed to be shot indoors. The box itself worked as a target stand and backstop for toy birds that could be attached to the box. You could also shoot at three bullseye targets printed inside the lid.