The Maw is set in a futuristic universe. The game begins with Frank, a pacifist bipedal alien, and The Maw, a purple one-eyed creature with large teeth, both having been captured by the Galactic Bounty Hunters. For unknown reasons the ship on which they are being held crash lands on a strange planet, killing all the crew. Alone, they set out for a communications tower in the distance while on the run from additional Galactic Bounty Hunters who have come to recapture them.