In a large pot or Dutch oven, heat olive oil over medium heat. Add onion, carrots, and celery and cook until softened, about 5-7 minutes.
Add chicken broth, chicken breasts, thyme, salt, and pepper to the pot. Bring to a boil, then reduce heat and simmer for 20-25 minutes, or until chicken is cooked through.
Remove chicken from the pot and shred with two forks. Return shredded chicken to the pot.
Add cannellini beans to the pot and heat through.
Stir in parsley and cilantro.
Serve hot with chimichurri, green onions, and additional cilantro for garnish.