Preheat the oven's broiler and set the oven rack about 6 inches from the heat source. Line a 10x12 inch pan with aluminum foil.
Use the tip of a sharp boning or paring knife to cut 3 small slits into the side of each chicken breast; insert a slice of garlic into each slit.
Mix the rosemary, thyme, and sage together on a shallow dish; roll and press each chicken breast into the herb mixture to coat.
Arrange the breasts close together on the foil-lined pan. Place carrots and red potatoes in a layer around chicken and fold up edges of foil approximately 1 inch. Drizzle carrots and red potatoes with olive oil, salt, and pepper.
Cook in the preheated oven for 7 minutes; turn the chicken and cook until no longer pink in the center and the juices run clear, 7 to 10 minutes more. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C).
