Heat olive oil in a large pot over medium-high heat. Add chicken pieces and cook until browned.
Add carrots, celery, and onion to the pot and cook until the vegetables start to soften, about 5 minutes.
Stir in garlic and cook for another minute. Add flour and stir to coat the chicken and vegetables.
Gradually stir in the chicken broth, scraping up any browned bits from the bottom of the pot.
Add thyme and potatoes. Bring to a boil, then reduce heat to low, cover, and simmer for about 30 minutes or until the chicken and vegetables are tender.
Season with salt and pepper to taste before serving.