Step 1, In a large pot over medium heat, melt butter. Cook onion and celery in butter until just tender, 5 minutes. Pour in chicken and vegetable broths and stir in chicken, noodles, carrots, basil, oregano, salt and pepper. Bring to a boil, then reduce heat and simmer 20 minutes before serving.
Stir chicken into the simmering broth; cook until the chicken is no longer pink in the middle, 5 to 10 minutes. Remove and discard bay leaf. Stir rice and lime juice into the broth; cook and stir just until rice is hot and grains separate, about 1 minute. Garnish with lime slices.