Preheat the oven to 375°F.
In a mixing bowl, combine the chopped spinach, diced roasted red peppers, mozzarella cheese, cream cheese, minced garlic, Italian seasoning, salt, and black pepper. Mix until well combined.
Using a sharp knife, create a pocket in each chicken breast by slicing horizontally, being careful not to cut all the way through.
Stuff each chicken breast with the cheese and vegetable mixture, securing the opening with toothpicks if necessary.
In a large oven-safe skillet, heat the olive oil over medium-high heat. Add the stuffed chicken breasts and sear for about 4-5 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 the chicken rest for 5 minutes before serving.