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Season the chicken breasts with the kosher salt and black pepper. Lay them in the bottom of a crock pot.
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Whisk together the lime juice with the dried thyme, dried oregano and dried onion. Add the minced clove of garlic, then whisk in the melted butter. Pour this mixture over the chicken breasts.
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Turn the crock pot to high and cover the pot. Let the chicken begin to simmer in the lime juice and butter, about 30 minutes, then add the chicken broth and reduce the temperature to low.
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Cook for 6 to 7 hours. Add the 2 cups of instant rice during the last 15 minutes of cooking time.