In a medium heavy skillet, saute the onions, garlic, and peppers in 2 tablespoons oil until soft. Add the chili peppers and tomatoes and simmer for a few minutes more. Add the chicken and stir well to combine. Heat a thin layer of oil in a heavy medium sized pan over medium low heat. Place a tortilla in the pan and sprinkle with 1/4 cup cheese. Add about 1/4 of the chicken mixture and top with another 1/4 cup cheese. Cover with another tortilla and cook for 2-3 minutes or until golden brown. Flip the quesadilla over and cook for an additional two minutes. Remove from heat and cut into wedges.
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