Remove and discard giblets and neck from chicken. Rinse chicken with cold water, and pat dry. Trim excess fat. Place chicken, breast side down, on a cutting surface. Cut chicken in half lengthwise along backbone (do not cut through breastbone). Turn chicken over. Starting at neck cavity, loosen skin from breast and drumsticks by inserting fingers, gently pushing between skin and meat.
Combine parsley, thyme, juice, salt, and pepper; rub mixture under loosened skin and over breast and drumsticks. Gently press skin to secure. Place chicken in a large zip-top plastic bag. Seal and marinate in refrigerator 30 minutes.
Preheat grill to medium heat.
Place chicken, skin side up, on grill rack coated with cooking spray. Grill 55 minutes or until a thermometer inserted into meaty part of thigh registers 180°. Remove chicken from grill; cover and let stand 10 minutes. Remove and discard the skin.