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Pre-heat the broiler.
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Pound chicken breasts to flatten slightly.
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Heat oil in a nonstick skillet.
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Add chicken and sautee over medium-high heat until browned on both sides, about 10 minutes.
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Transfer to a broiler pan.
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Divide pesto among chicken breasts, spreading almost to the edge.
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Top with cheese slices and grill just until cheese has melted.