In a medium heavy skillet sauté the onions, garlic, and peppers in the 2 Tbsp. 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 the heat and cut into wedges.
Keep warm while frying the remaining quesadillas. Serve with salsa and sour cream.