Preheat oven to 400°F. Place pizza crust on baking sheet, brush lightly with small amount of olive oil. Bake 5 minutes. Remove from oven, leaving oven on.
Meanwhile, cut chicken breasts into 1/2-inch wide strips; sprinkle lightly with salt and black pepper to taste. In medium skillet heat remaining oil over medium-high heat. Add chicken; cook and stir 3 to 5 minutes or until chicken is no longer pink.
Meanwhile spread barbecue sauce on heated crust. Top with onions, red peppers, chicken, and cheese. Bake 15 to 20 minutes or until hot and cheese is melted and lightly browned.
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