Preheat your oven to 375°F.
Using a sharp knife, create a pocket in each chicken breast by slicing horizontally, being careful not to cut all the way through.
In a bowl, combine the diced apple, Brie cheese, and thyme. Season with salt and pepper.
Stuff each chicken breast with the apple and Brie mixture, securing the opening with toothpicks if necessary.
In an oven-safe skillet, heat the olive oil over medium-high heat. Sear the stuffed chicken breasts for about 3-4 minutes on each side until golden brown.
Pour the chicken broth and balsamic vinegar into the skillet around the chicken. Bring to a simmer, then transfer the skillet to the preheated oven.
Bake for 25-30 minutes or until the chicken is cooked through and reaches an internal temperature of 165°F.
Remove the skillet from the oven and let the chicken rest for 5 minutes before serving.