Heat olive oil in a large pot over medium heat.
Add onion and garlic, sauté until fragrant, about 2-3 minutes.
Stir in carrots and celery, cook for another 5 minutes.
Add chicken thighs and pour in chicken broth.
Add potatoes, thyme, salt, and pepper. Stir to combine.
Bring to a boil, then reduce heat and simmer for 30 minutes, or until chicken and potatoes are tender.
Remove chicken, shred it with two forks, then return to the pot.
Simmer an additional 5 minutes. Adjust seasoning as needed.
Serve hot, garnished with fresh parsley.