In an 8-quart saucepan or pot over medium-high heat, heat oil. Add chicken and cook, turning occasionally, until browned, about 4 minutes. Transfer chicken to a plate and set aside. Return the saucepan to the heat and stir in the onion, celery, parsnip, thyme and parsley. Cook, stirring occasionally, until vegetables are just starting to soften, about 3 minutes. Add the reserved chicken and broth. Bring to boiling then reduce heat to medium-low, cover and simmer until chicken and vegetables are very tender, about 40 minutes.