Heat 1 tablespoon olive oil in a large skillet over medium heat until the oil shimmers.
Add 1 ½ cups diced onion, 1 cup diced carrot, and ⅓ cup diced celery. Cook, stirring occasionally, 2–3 minutes, until the vegetables begin to soften.
While the vegetables cook, slice 1 pound boneless, skinless chicken breasts into strips.
Add the chicken strips to the skillet and cook, stirring occasionally, about 5–6 minutes, until the chicken is no longer pink in the center and is cooked through.
Stir in 1 (14.5-ounce) can crushed tomatoes with basil, oregano, and garlic, ¼ cup grated Parmesan cheese, 1 tablespoon chopped fresh basil, ½ teaspoon salt, and ¼ teaspoon ground black pepper.
Bring the mixture to a gentle boil, then reduce the heat to medium-low and simmer, uncovered, about 10 minutes, stirring occasionally.
Remove from heat and serve.