1. Combine lime juice, olive oil, oregano, salt and pepper in a large container. Place chicken in the mixture and marinate for 2 hours.
2. Meanwhile, place beans, water, garlic, and salt in a saucepan and bring to a boil. Once it has boiled, reduce heat and let simmer for an hour and a half.
3. Heat oven to 350. Line a glass baking dish with onion, and place chicken breasts on top. Bake for 15 minutes. While the chicken is baking, heat some oil in a cast-iron skillet.
4. Remove bean mixture from heat and pour off water until there is just enough left to cover the beans. Put the remaining mixture in a food processor and pulse until it is mixed, but there are still large chunks of bean left.
5. Remove the chicken from the oven and place in cast iron skillet. Grill about 2 minutes on each side, or until brown and done. Serve over the onions with some rice and bean sauce.
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