Rinse the chicken and pat dry, trim off any fat. With a sharp knife (I use a boning knife) cut a slit into each breast to create a pocket, making sure not to cut all the way through. Season lightly with salt and pepper on both sides plus inside the pocket.
In a small bowl whisk together the olive oil, maple syrup, Dijon mustard, thyme, 1 tsp. salt, and two pinches pepper. Rub half of this marinade all over the chicken, both sides plus inside the pocket. Allow this to sit and soak in while making other preparations or marinade the chicken earlier in the day to sit in the fridge.
Preheat the oven to 400 degrees. Stuff each pocket with a nice thick slice of brie and the sliced apples. Sear the chicken in a pan with olive oil until both sides are golden brown. Transfer to a baking dish and divide the remaining marinade over each chicken breast. Finish cooking in the oven for about 15 minutes or until the internal temperature reaches 165 degrees.
Allow the chicken to rest before plating. Deglaze the pan with a little water, chicken broth, or white wine and cook until it reduces to a nice glaze. Drizzle the glaze over the chicken once plated.
