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. Place 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 350F 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 400F without BBQ sauce for the 20 minutes. Turn once to help cook the bacon. Reduce heat to 375F, change pans to lose some of the bacon fat, cover with BBQ sauce and finish baking for 10 minutes (broil fro the last 3 minutes to set the BBQ sauce).