If using wooden skewers, place in water and soak for at least one hour.
Cut chicken into 1-inch dice. In a small bowl, whisk together mustard, vinegar, thyme, salt, pepper, and zest. Slowly whisk in olive oil to combine.
Thread chicken, zucchini rounds, mushrooms, and peach slices onto skewers, alternating ingredients. Be sure to leave enough space at bottom of skewer to hold and turn.
Place skewers in a single layer on a sheet pan or baking dish and pour marinade over, turning skewers to distribute marinade. Cover with plastic wrap or aluminum foil and refrigerate. Marinate, turning skewers occasionally, for at least 30 minutes or overnight.
Heat grill on high heat. Place skewers on grill and cook, turning, for about 10 minutes.
Serve over rice.