Preheat your oven to 375°F (190°C).
Prepare the stuffing by mixing brie cheese, chopped apple, walnuts, thyme, and a pinch of salt and pepper in a bowl.
Make a pocket in each chicken breast by slicing it horizontally without cutting all the way through.
Stuff each chicken breast with the apple-brie mixture, then secure it with toothpicks if necessary.
Season the chicken with salt and pepper on both sides.
Heat olive oil in a large oven-safe skillet over medium-high heat and sear the stuffed chicken breasts until golden brown on each side.
Transfer the skillet to the preheated oven and bake for 20-25 minutes, or until the chicken is cooked through.
Remove from the oven, rest for 5 minutes, and serve warm.