Heat the olive oil in a large soup pot over medium heat. Add the onion, and sauté for 2 minutes or until starting to soften. Add the celery and carrots, and continue cooking for approximately 5 minutes, or until the carrots are just beginning to soften, stirring occasionally.
Add the chicken broth, increase the heat, and bring to a boil. Reduce the heat to a simmer and cook, uncovered, about 10 minutes more or until carrots are just tender.
Stir in the rice, chicken, and parsley. Cook for a few more minutes or until heated through. Season the soup with salt and pepper, to taste. (When using store-bought broth, I typically do not add salt. When using homemade stock, I add 1 1/2 to 2 teaspoons of kosher salt.)