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 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.
Bake for 20 minutes or until chicken is done. Finish under the broiler to set the BBQ sauce, turning once to help cook the bacon.
Then turn heat to broil, change pans to loose some of the bacon fat, cover with BBQ sauce and finish baking/broiling.