Preheat oven to 425.
Combine 1 tablespoons butter, thyme, and blue cheese in small bowl until blended. Season with salt & pepper and set aside.
Cut a horizontal line in the thickest side of each chicken breast to form a pocket, but not cutting all the way through. Stuff blue cheese mixture into pocket with small spoon. Place chicken in a baking dish. Season with salt & pepper. Bake 15 minutes, uncovered.
Remove from oven and turn chicken, and brush with balsamic sauce. Bake additional 10 to 15 minutes or until chicken is cooked through (use thermometer in unstuffed area).
During last 10 minutes, place remaining Strawberry Balsamic Sauce in a small pot and reduce to a slightly thick sauce. Drizzle cooked chicken with sauce and serve.