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Preheat oven to 350 degrees F.
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Heat the oil in skillet and add the chicken and onion. Cook 15 minutes or until the chicken is browned and just about done. Add salt and pepper to taste.
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Place the chicken on a cookie sheet and top each breast with 1 to 2 slices of tomato and 2 to 3 slices of cheese. Place in the oven for 10 to 15 minutes, until the cheese melts.
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Remove from the oven, add 2 to 3 slices of avocado on top of each breast, and serve immediately.