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Heat a grill to medium high (about 450° to 500°F).
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Roll out dough into a circular or rectangular shape.
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Place dough on a pizza peel (sprinkle pizza peel first with cornmeal for easier sliding of dough).
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Use tongs to dip a paper towel into a small bowl of olive oil then brush grates with oil.
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Slide the dough from the pizza peel onto the grill grates. Cover and grill for about 2 minutes, until bottom has lightly browned.
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Use tongs to remove dough and place upside down on the pizza peel.
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Brush uncooked side of dough with olive oil.
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Spread a thin layer of sauce over dough. Top with chicken, mozzarella cheese, and parmesan cheese.
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Return pizza to the grill. Cover and cook about 2 to 3 minutes, until cheese has melted and bottom of crust has browned.
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Top pizza with arugula and sliced tomatoes.
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Drizzle with olive oil and white wine vinegar (if using).