In a large resealable plastic bag, combine the oil, dill, oregano, lemon peel, garlic, salt and pepper; add chicken. Seal bag and turn to coat; refrigerate for at least 2 hours.
Using a vegetable peeler, peel bark from the bottom half of each rosemary stem and make a point at each end; soak in water until ready to use.
Drain and discard marinade. On soaked rosemary stems, alternately thread the chicken, artichokes, squash and tomatoes. Position the leaf parts of the rosemary stems so they are outside of the grill cover.
Using long-handled tongs, moisten a paper towel with cooking oil and lightly coat the grill rack. Grill, covered, over medium heat or broil 4 in. from the heat for 10-15 minutes on each side or until chicken is no longer pink and vegetables are tender. Yield: 6 servings.