Heat 1 tablespoon olive oil in a large skillet over medium heat.
Add the diced onion, diced carrot, and diced celery to the skillet and cook, stirring occasionally, for 2–3 minutes until the vegetables begin to soften.
While the vegetables cook, slice the chicken breasts into strips.
Add the chicken strips to the skillet and cook for 5–6 minutes, stirring occasionally, until the chicken is no longer pink on the outside.
Stir in the can of crushed tomatoes, grated parmesan, chopped fresh basil, salt, and black pepper; bring the mixture to a boil.
Reduce heat to medium-low and simmer for about 10 minutes, until the sauce is slightly reduced and the chicken is cooked through.
Serve the Tuscan basil chicken over rice or pasta if desired.