Heat large heavy pot on medium. Peel and shred carrots, peel and smash garlic cloves, and dice onion.
Once pot is hot, add olive oil. Add carrots, onion, and garlic. Stir periodically, but let sit for 10 minutes.
Once carrots are soft and have changed color, sprinkle flour and parsley on top. Stir, then let it cook for 2 minutes.
Add chicken stock slowly, stirring constantly to avoid lumps. Let it simmer for 10-15 minutes, then puree with immersion blender.
If you don't have one, use a regular blender, but please follow the usual safety precautions: don't fill it more than ⅓ full of hot liquid at a time, and always use a kitchen towel or an oven mitt to protect your hand while you hold the lid on.
Add chicken and stir, then add salt and pepper to taste. Serve immediately
