Preheat oven to 375 degrees F.
Heat oil in a large skillet over medium heat.
Add the onion and cook about 3 minutes.
Add the garlic and the chicken and cook until browned.
Add the salt, pepper, cayenne, and vinegar, stir to coat.
Fill the pepper halves with the chicken mixture and lay in a baking dish.
Add 4 Tbsps of water to the bottom of the dish and cover tightly with foil. Bake for 25 minutes.
Remove the cover and top each with a half slice of provolone. Place back in the oven uncovered, and broil until cheese is browned and bubbly, 4-5 more minutes.