Lightly oil the grill rack and heat the grill to medium. Grill the chicken for 15 minutes or until the chicken is cooked through, turning the chicken halfway through grilling. Remove the chicken to a cutting surface. Let cool for 5 minutes. Cut into strips. Set aside.
Heat the oil in a 6-quart saucepot over medium heat. Add the onions, carrots, parsnips and fennel and cook for 5 minutes or until the vegetables are tender. Add the broth and heat to a boil. Reduce the heat to medium-low and cook for 30 minutes or until the vegetables are very tender.
Stir in the chicken, peas and parsley and heat through. Season to taste. Divide the soup mixture among 8 serving bowls.