Preheat the oven to 425°F.
Slice 6–7 deep Hasselback-style slits across each chicken breast, being careful not to cut through. Season with salt and pepper. Set aside while to quickly dry brine you prepare the rest of your ingredients.
Make the chestnut–brie mixture by combining the softened brie, chopped chestnuts, salt, balsamic vinegar and nutmeg.. Keep the mixture rustic and textured. I use a fork to mash the finely chopped chestnuts into it but you can also use clean hands.
Gently stuff each slit with a small amount of the chestnut–brie mixture. Don’t overpack. Tuck a strip of prosciutto into each slit alongside the filling. Gently squeeze the chicken breast from top to bottom to make sure it keeps its form and each slit slightly sticks together.
If you have extra chestnut–brie mixture, tuck it between the slits or underneath the chicken.
Bake at 425°F for 20–25 minutes, or until the chicken is cooked through and the brie is bubbling and golden.
Finish with grated chestnut, fresh thyme, and any pan juices. Serve warm.