Preheat oven to 350 degrees F. Loosen the skin on one edge of each chicken breast half. Using 3 tablespoons of the total pesto, rub about 2 teaspoons pesto under and over the skin of the each breast half. Arrange chicken in a 15X10X1-inch baking pan. Bake, uncovered, for 45 to 55 minutes or until chicken is no longer pink (170 degrees F). Remove chicken from oven; cover and keep warm.
Preheat broiler. Place sliced zucchini on the unheated rack of a broiler pan. Brush both sides with oil and sprinkle with the salt and pepper. Broil about 4 inches from the heat for 8 to 10 minutes or just until tender, turning once halfway through broiling. Cut squash into 1/4-inch slices. Toss with the remaining 1 tablespoon pesto. Serve with chicken.