To make the sauce: In a medium saucepan over medium heat, melt the butter. Add the onion and cook until soft, 3 to 4 minutes, stirring occasionally. Add the remaining sauce ingredients. Stir and cook for about 3 minutes.
Lightly brush or spray the chicken on both sides with oil and season with salt and pepper to taste. Grill over direct medium heat until the meat is firm to the touch and no longer pink in the center, 8 to 12 minutes, turning once. Remove from the grill and let rest for 3 to 5 minutes. Shred the chicken, add to the sauce, and heat through over medium heat.
Grill the rolls over direct medium heat until lightly toasted, 30 to 60 seconds. Build each sandwich with a roll and some shredded chicken.
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