Slice chicken breasts in half (like a hamburger bun). Place in a plastic food bag and pound until 1/4 thick. Season with salt and pepper.
Mix the 2 cheeses together and smear about 1 tablespoons into each pepper half (use up the cheese between all of the peppers).
Place the pepper on the chicken breast and wrap it up as best you can. I suggest placing the pepper cheese side down so it gets completely covered by the chicken. Wrap each chicken breast completely with two pieces of bacon. Start at one end, wrap half the breast and finish the 2nd half with the other piece of bacon.
Cook on a preheated 350 degree grill over indirect for 30 minutes or until chicken is done. Turn every 5 minutes and baste with barbecue sauce each time you turn it.
For oven: Bake at 375 degrees for 30 minutes or until chicken is done. Baste a couple times with the barbecue sauce and finish under the broiler to set the BBQ sauce. ~~I suggest a 400 degree oven and no BBQ sauce for the first 20 minutes, turning once to help cook the bacon. Then reduce heat to 375, change pans to loose some of the bacon fat, cover with BBQ sauce and and finish baking/broiling.