1. In a small bowl, stir together lemon juice, olive oil, parsley, garlic, dill and pepper. Season to taste with Herbamare.
2. Put the chicken in a large plastic zip bag. Put the pieces of zucchini, squash, onion and bell pepper in another bag. Divide the marinade between the two bags. Seal the bags, turn them over to make sure the contents are coated, and refrigerate for at least 6 hours and up to 12 hours, turning them periodically.
3. Prepare a charcoal or gas grill. Lay a sheet of aluminum foil over the grill rack to keep the chicken and vegetables from burning. The coals or heating elements are ready when they are medium-hot.
4. Lift the vegetables from the plastic bag, letting any excess marinade drip back into the bag and transfer them to the grill. Reserve the marinade. Cook for about 30 minutes total; the squash may cook faster than the onions, and the onions may be done before the peppers. Watch carefully, and turn the vegetables several times and brush them with the marinade during grilling. Transfer the grilled vegetables to a platter.
5. Lift the breast halves from the plastic bag, letting any excess marinade drip back into the bag, and transfer them to the grill. Discard the marinade. Cook for 6-7 minutes on each side, turning once.