Heat olive oil in a large pot over medium heat.
Add chopped onions, carrots, and celery; sauté until soft.
Stir in minced garlic and cook for an additional minute.
Add chicken breasts to the pot and pour in the chicken broth.
Bring to a boil, then reduce heat and simmer for 15 minutes.
Remove chicken breasts, shred them, and return to the pot.
Add thyme, salt, and pepper to taste.
Pour in the heavy cream and stir well.
Simmer for another 5-10 minutes until heated through.
Serve hot, garnished with fresh herbs if desired.