Preheat the oven to 450 degrees F. Line a baking sheet or roasting pan with aluminum foil.
Create a pocket under the skin of each chicken breast by gently separating the skin from the flesh, with a spoon or fingers. Try to leave the sides attached as much as possible to prevent the cheese from oozing out.
Using a spoon or your hands, stuff about 2 tablespoons of Boursin under the skin of each chicken breast. Replace the skin and squish around to evenly distribute the cheese.
Place the breasts onto the lined baking sheet and roast for 20-30 minutes until chicken is no longer pink. Bone-in breasts will take a bit longer than boneless.