Season the chicken breasts with salt, pepper, and Italian herbs on both sides. Set aside.
Heat the olive oil in a large skillet over medium-high heat.
Add the seasoned chicken breasts to the skillet and sear each side for about 4-5 minutes, until they are golden brown.
Prepare the vegetables by slicing the bell peppers and onion, and placing them in a bowl with the cherry tomatoes.
After the chicken is seared, add the mixed vegetables around the chicken in the skillet.
Pour the balsamic vinegar over the chicken and vegetables, gently tossing the vegetables to coat them in the sauce.
Reduce the heat to medium and cover the skillet with a lid. Cook for an additional 20 minutes, or until the chicken is cooked through (internal temperature should reach 165°F).
Remove the lid and let the dish sit for a few minutes. Adjust seasoning with additional salt and pepper if needed.
Serve hot, garnished with fresh basil leaves if desired.