Heat 1 teaspoon of olive oil in a large nonstick skillet over medium heat.
Add the diced chicken, season with ¼ teaspoon each of salt and pepper, and cook for about 5 minutes until just cooked through. Transfer to a bowl and set aside.
While the chicken cooks, bring a large pot of salted water to a boil and cook the penne according to package directions. Drain and set aside.
For the sauce, heat 2 teaspoons of olive oil in the same skillet. Add the onion and carrots and sauté for about 5 minutes until softened.
Stir in the minced garlic, oregano, red pepper flakes, and another ¼ teaspoon each of salt and pepper. Cook for 1 minute until fragrant.
Pour in the crushed tomatoes and bring the sauce to a boil, then lower the heat to a simmer. Cook for 10 minutes, stirring occasionally.
Stir in the parsley and basil, then add the cooked chicken and penne back into the skillet. Toss everything to coat evenly in the sauce.
Season to taste with additional salt and pepper if needed. Serve hot with grated Parmesan cheese, if desired.