Preheat oven to 350°.
Remove white papery skin from garlic head (do not peel or separate the cloves). Wrap head in foil. Bake at 350° for 1 hour; cool 10 minutes. Separate cloves; squeeze to extract garlic pulp. Discard skins. Combine garlic pulp and cheese, stirring well; set aside.
Cut a horizontal slit through thickest portion of each chicken breast half to form a pocket. Stuff about 4 teaspoons cheese mixture into each pocket. Sprinkle chicken evenly on both sides with salt and pepper.
Heat oil in a large ovenproof skillet over medium-high heat. Add chicken to pan; cook 3 minutes or until lightly browned. Turn chicken over. Bake at 350° for 20 minutes or until a thermometer registers 165°; let stand 5 minutes.