Heat large covered saucepot of salted water to boiling on high. Add pasta and cook as label directs.
Meanwhile, in 12-inch nonstick skillet, heat 2 teaspoons oil on medium 1 minute. Add ground chicken to skillet; sprinkle with 1/4 teaspoon salt. Cook chicken 8 to 9 minutes, or until it is no longer pink, stirring occasionally. Transfer chicken along with any juices in skillet to medium bowl.
To same skillet, add remaining 2 teaspoons oil with carrots, celery, onion, and garlic; cook 10 to 12 minutes or until vegetables are lightly browned and tender, stirring occasionally. Stir in tomatoes, 1/4 teaspoon salt, and 1/4 teaspoon freshly ground black pepper; heat to boiling. Reduce heat to medium-low and simmer, uncovered, 10 minutes, stirring occasionally. Stir in cooked chicken and milk; heat through.
Reserve 1/4 cup pasta cooking water. Drain pasta and return to saucepot; stir in sauce from skillet, Parmesan, parsley, and reserved cooking water, and toss to coat.