Heat olive oil in a large pot or Dutch oven over medium heat. Sauté onion, carrots, and celery until softened, about 5 minutes.
Add minced garlic and cook for 1 minute until fragrant.
Pour in chicken broth and bring to a simmer. Add chicken breasts and cook for 15-20 minutes, or until fully cooked.
Remove chicken from the pot and shred using two forks. Return shredded chicken to the pot.
Add gnocchi and simmer for 10 minutes, or until tender.
Stir in heavy cream, thyme, salt, and pepper. Simmer for an additional 5 minutes.
Serve hot, garnished with fresh parsley or Parmesan cheese if desired.