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Combine lime juice, vegetable oil, red pper, and garlic in a large zip-top heavy-duty plastic bag.
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Add chicken; seal bag, and marinate in refrigerator 8 hours, turning bag occasionally.
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Bring water to a boil in a small saucepan; add bell pepper and onion.
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Cook 30 seconds; drain.
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Plunge into ice water; drain well.
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Set aside.
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In a food processor, add beans, orange juice, balsamic vinegar, salt, pepper, and garlic.
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Process until smooth.
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Pour into a saucepan; cook over medium-low heat until heated.
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Remove chicken from bag and grill over medium-hot coals.
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Cook 8-10 minutes on each side or until chicken is done.
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To serve, divide bean mixture onto each of 4 plates.
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Place chicken breast on top of sauce; top each with 2 tablespoons bell pepper mixture or a fresh tomato salsa.