Brush chicken breasts with olive oil, season with salt, pepper and chilies. Place on grill on MEDIUM, and turn only once until breasts are cooked thoroughly. Slice thinly.
Place whole red peppers on grill to cook until hot, yet not completely cooked. Cool slightly, then thinly slice the peppers, green onions, and mushrooms. Toss with remaining olive oil, red chili, coriander and salt and pepper. Pour out excess oil, cover, and set aside.
Brush the pizza crust with chili oil. Place chicken evenly over the crust, then sprinkle with vegetables and top with shredded mozzarella cheese.
Cook pizza on a preheated barbecue on LOW for 5-10 minutes or until the base is crisp and golden and the cheese is bubbling. Slice and serve hot.
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