Warm oil in a skillet over medium heat. Add chicken and cook, turning once, 5 to 6 minutes per side, until just cooked through. Transfer to a cutting board. When cool enough to handle, cut into 1/2-inch cubes. Toss chicken with 2 Tbsp. barbecue sauce in a bowl.
Position a rack in bottom of oven and preheat to 450°F. Place pizza crust on a large baking sheet and spread with remaining 1/2 cup barbecue sauce. Sprinkle with half of both cheeses, arrange chicken on top, and then add remaining cheese and onion.
Bake until cheese is melted and golden brown, 20 minutes. Let rest for 5 minutes. Sprinkle with cilantro, cut into slices and serve hot.