In a medium saucepan, combine the chicken breasts, chicken broth, thyme, oregano, rosemary, garlic, salt, and black pepper. Bring to a boil, then reduce heat and let simmer for 1 hour.

In a large pot, heat olive oil over medium heat. Sauté chopped onion until caramelized, then add carrots and celery and mix well before turning off the heat.

Remove chicken from saucepan, allow to cool, then shred using two forks. Strain the cooking liquid and reserve the broth.

In the large pot, combine shredded chicken with reserved broth and sautéed vegetables. Adjust seasoning with additional salt and pepper.

Bring the mixture to a simmer, stirring occasionally until the carrots and celery are tender. Stir in chopped parsley, dill, and basil just before serving.