Preheat the oven to 375°F.
Using a sharp knife, carefully cut a pocket into each chicken breast, being careful not to cut all the way through.
In a bowl, mix together the roasted red peppers, goat cheese, basil, garlic powder, onion powder, salt, and pepper until well combined.
Stuff each chicken breast pocket with the goat cheese mixture, securing with toothpicks if necessary.
In a large oven-safe skillet, heat the olive oil over medium-high heat. Sear the stuffed chicken breasts for 3-4 minutes on each side until golden brown.
Drizzle the balsamic vinegar over the chicken, then transfer the skillet to the preheated oven.
Bake for 20-25 minutes, or until the chicken is cooked through and reaches an internal temperature of 165°F.
Remove from the oven and let rest for 5 minutes before slicing.