Melt the butter over medium heat in a large pot or dutch oven. Add chopped onion, sliced celery, and sliced carrots. Cook until the vegetables are soft and fragrant, about 8–10 minutes, stirring occasionally.
Pour in chicken broth or homemade stock. Add salt and black pepper, adjusting to taste. Bring the mixture to a gentle boil over medium heat.
Stir in diced chicken breasts. Simmer for 10 minutes, letting flavors blend together.
Reduce heat to low. Stir in the cooked rice and fresh parsley. Simmer just until everything is heated through.
Ladle hot soup into bowls to serve. If desired, squeeze in a little lemon juice or lime juice to brighten the flavor.