1. In a large pot, heat olive oil over medium heat. Add the chicken breasts and cook until browned on both sides, about 5-7 minutes. Remove from pot and set aside.
2. In the same pot, add onions and garlic. Sauté until onions are translucent.
3. Add carrots and celery, cooking for another 5 minutes.
4. Pour in the chicken broth and bring to a simmer.
5. Shred the cooked chicken and return it to the pot.
6. Stir in heavy cream, thyme, salt, and pepper. Let simmer for an additional 10 minutes.
7. Serve hot, garnished with fresh parsley.