Preheat oven to 350°F. Brown chicken in oil in a heavy, lidded skillet. Add onions and celery; cook until softened.
Add wine, then sprinkle in tarragon, salt, and pepper. Tuck in garlic cloves. Cover and bake ~30 minutes.
Reduce oven to 300°F and continue baking 45–60 minutes, basting every 15 minutes. Add basil and lemon juice; adjust seasoning and garnish with parsley. Serve with bread, rice, or potatoes.