Preheat the grill to medium high (375 degrees F) and set up for indirect cooking.
Remove the “goodies” from inside the chicken (and the pop-up thermometer if there is one). Rinse and dry the chicken thoroughly with paper towels. Rub olive oil over outside of chicken. Rub the Cajun spice and crushed rosemary all over the outside of the chicken.
Put the chopped vegetables in the bottom of a roasting pan. Add two cups of chicken stock and the peppercorns. Put the chicken on a roasting rack in the pan, put the pan on the unheated side of the cooking grate, and roast for 20 minutes per pound or until the thigh has an internal temperature of 165 degrees F.
Let the chicken rest for 10 minutes before carving.
