Heat a small skillet over medium-high heat. Melt butter and saute chopped fennel for about 5 minutes to soften.
While the fennel is cooking, pound of your chicken breasts until they are 1/4-inch to 1/2-inch thick.
In a mixing bowl, combine fennel with bell pepper and artichoke hearts.
Spoon the fennel mixture into the center of each chicken breast. Sprinkle with mozzarella cheese. Fold chicken over and secure with toothpicks so that the filling is trapped inside. Place stuffed chicken breasts into a lightly greased 9x13 pan.
In a small mixing bowl, whisk together balsamic vinegar, olive oil, basil, salt, pepper, and crushed garlic. Pour over chicken breasts.
Bake at 400 degrees for 30-40 minutes, until chicken reaches an internal temperature of 165 degrees F.