Preheat the oven to 375°F.
Using a sharp knife, carefully create a pocket in each chicken breast by slicing horizontally, being careful not to cut all the way through.
In a small bowl, combine the diced apple, Brie cheese, and thyme. Season with salt and pepper.
Stuff each chicken breast pocket with the apple and Brie mixture, securing the opening with toothpicks if necessary.
Heat the olive oil in an oven-safe skillet over medium-high heat. Add the stuffed chicken breasts and sear for about 3-4 minutes on each side until golden brown.
Pour the chicken broth and balsamic vinegar into the skillet, then transfer the skillet to the preheated oven. Bake for 20-25 minutes, or until the chicken is cooked through (internal temperature should reach 165°F).
Remove the skillet from the oven and let the chicken rest for 5 minutes before slicing.