Combine cream cheese and shredded jalapeño cheese in a small bowl.
Dice jalapeños and stir into cheese mixture.
Cut a pocket into each chicken breast. Make sure not to filet the breast open too far or cut through the bottom. You will want to create a deep pocket that you can close back up.
Spoon the cheese into the chicken pocket. I use the back of the spoon to press in as much as possible.
Manipulate the chicken so that even with a bulge of cheese filling, you can mostly close the chicken back up.
Wrap each breast with two strips of bacon.
Brush chicken with BBQ sauce. (This step can be done before cooking or after… or both!)
Grill: Preheat grill on high. Add wrapped chicken breasts. Turn heat down to low-medium. Cook for 10-15 minutes per side. (Note: grilling may cause cheese to ooze out into grill.)
Oven: Bake uncovered at 350 degrees F (175 degrees C) for 30 to 35 minutes.
Serve breasts by halves or slice on an angle in 1” segments and fan out on serving platter or plate.