Preheat oven to 375 degrees. Coat a roasting rack with nonstick spray and set in roasting pan.
In a large skillet over medium-high heat, heat olive oil until shimmering. Add onion, celery, and olives and cook until celery is tender, about 5 minutes.
Starting at the back opening of the chicken, use your fingers to carefully separate the skin from the meat on the chicken breast and thighs. Be careful not to tear skin. Spread about 1/4 cup pesto sauce between the skin and meat of the chicken.
Fold wings of chicken across back with tips touching. Spoon onion mixture into cavity of chicken, then tie or skewer drumsticks to tail.
Place chicken, breast side up, on a rack in a shallow roasting pan. Brush chicken with half of remaining pesto. Roast uncovered 1 to 1 1/2 hours, brushing occasionally with remaining sauce, until a thermometer inserted near the thigh reaches 180 degrees.
Remove from oven. Let stand 15 minutes before carving.