DIAGNOSIS: Your crossover tube, the small tube that connects the burners together at the back, is probably clogged or the ports are blocked. This tube equalizes gas flow between the left and right burners.
FIX: Let the grill cool completely. Remove the cooking grates and flavorizer bars. You'll see the burners and a small horizontal tube connecting them at the rear. Use a stiff wire (a paperclip works) or a small drill bit turned by hand to gently clear out any spider webs, debris, or corrosion from the tiny holes along the top of that crossover tube.
IF THAT DIDN'T WORK: The burner tube itself on the cooler side might be partially blocked. Inspect the burner ports (the little holes along its length) for obstructions and clear them out the same way.
HEADS UP: Never use a power drill to clean these ports—you can easily enlarge them and mess up the gas/air mixture, leading to improper flames.