Combine first 5 ingredients in a large zip-top plastic bag. Add chicken; toss well to coat. Remove chicken from bag; reserve flour mixture. Melt butter in a large nonstick skillet over medium heat. Add chicken, breast sides down; sauté 5 minutes or until chicken is browned. Remove chicken from pan; keep warm.

Add onion, celery, and garlic to pan; sauté 5 minutes, stirring occasionally. Stir in reserved flour mixture; cook 1 minute. Add broth and wine; bring to a boil. Add carrot. Return chicken to pan, breast sides up. Cover, reduce heat, and simmer 25 minutes or until chicken is done. Sprinkle with the chopped parsley.