2. Heat 2 teaspoons olive oil in a skillet over a medium-high heat. Cook the bell pepper mixture until tender, about 4 to 5 minutes.
3. Cut a deep horizontal pocket in the side of each chicken breast. Make the pocket as large as you can without piercing the top or bottom of the breast. Place 1/4 cup of the pepper mixture in the pocket of each chicken breast. Secure the pocket with toothpicks threading along the side to close.
4. Heat the remaing 1 1/2 tablespoons oil in a heavy oven-proof skillet until it begins to smoke. Cook each side of the chicken until golden brown.
5. Add the vinegar and chicken stock and bring to a boil. Lower the heat and gently simmer the chicken for 2 or 3 minutes per side until cooked through.
6. Remove the chicken breasts from the skillet and keep warm. Continue to cook the sauce until it is reduced to a thick syrup.
7. Taste the sauce and season with salt and pepper. Spoon the sauce over each chicken breast to serve.