Place chicken breast on cutting board, with one hand on top of chicken, parallel to cutting board. Insert knife 4 inches into middle of breast (widthwise), and make a 2 inch wide pocket. Repeat for each chicken breast.
Mix together goat cheese, blueberries, rosemary, minced garlic, and red pepper flakes.
Divide mixture into 4 parts and stuff each breast with filling. Seal each pocket with a few toothpicks.
Cook over medium/high heat in a greased saute pan, about 2 minutes on each side until brown (the inside will still be very raw).
Brush each piece (both sides) with ½ Tbsp of your favorite BBQ sauce.
Bake in oven at 375 degrees F for about 25 to 30 minutes (or until internal temperature of chicken reads 160 degrees F), flipping at the halfway point.
Remove from oven and let rest 5 minutes before cutting.