In a large pot, heat the olive oil over medium heat. Add the diced onion and sauté for about 3-4 minutes until translucent. Stir in the minced garlic and cook for an additional 1 minute until fragrant.
Add the carrots and celery to the pot, cooking for another 5 minutes until they begin to soften.
Stir in the chicken pieces and cook until they are no longer pink, about 5-7 minutes.
Pour in the chicken broth and add the diced potatoes, thyme, rosemary, salt, and pepper. Bring the mixture to a boil, then reduce the heat and let it simmer for 20-25 minutes, or until the potatoes are tender.
Once the potatoes are cooked, stir in the heavy cream and let the soup simmer for an additional 5 minutes. Adjust seasoning if necessary.
Serve hot, garnished with fresh parsley.