Preheat a grill to moderate high heat. Place the chicken between two sheets of plastic wrap and flatten slightly with a rolling pin or meat mallet. Remove meat from plastic. Grill meat about 10 minutes. Remove from heat and set aside for 5 minutes. Chop meat into 1/2 inch cubes
While meat is cooling, place a large sauté pan over moderate heat. Coat with cooking spray. When pan is hot, add the onions. Sauté for 5 minutes, until onions become tender. Add peppers and cook for 10 more minutes. Add vinegar to sauté pan, stir to scrape up any residue on the bottom of the pan, and remove from heat.
Divide meat and peppers between two buns. Top each with 2 half slices of cheese. Wrap the sandwiches in foil and return to grill for 2 minutes to melt the cheese.
