Heat oil in a large saucepan over medium heat. Add onion, carrots and celery. Sauté until softened, 5 minutes. Add stock, tomato, chicken breast, turnip and basil. Simmer, uncovered, until chicken is cooked through, 30 minutes.
Remove chicken from pan. Discard bones. Coarsely chop chicken. Return to soup with the noodles. Cook until noodles are tender, 4 minutes. Add pepper.