Preheat oven to 180 C / Gas mark 4. Heat 2 tbsp oil in a large frying pan over medium heat. Dredge chicken in flour, shaking off excess. Add a third of the chicken to the pan; sauté until golden brown, about 4 minutes each side. Transfer to a roasting tin. Sauté remaining chicken in two more batches, using 2 tbsp oil per batch. Transfer to a roasting tin.
Add garlic, celery, rosemary and thyme to the frying pan; cook 1 minute. Add vermouth or wine. Increase heat to high, bring to the boil and cook 2 minutes so the alcohol evaporates. Add the stock and salt to the tin; bring to the boil. Remove from heat. Pour vegetables and cooking liquid over chicken in roasting tin. Cover pan with aluminium foil.
Bake until chicken is cooked and garlic is meltingly tender, about 45 minutes. Serve chicken with a little of the garlic.