1 Prepare marinade, stirring together lime juice, rum, soy sauce, and sugar in a bowl until sugar has dissolved. Add the chicken to the marinade and let marinate for 30 minutes at room temperature (can marinate longer chilled, but allow to come to room temp for 30 minutes before cooking).
2 Pour enough oil in a skillet so that it comes up the sides at least a half an inch. Heat oil on medium high until it is shimmering, and a little pinch of flour sizzles when you drop it in the pan.
3 While the oil is heating, whisk together the flour, paprika, and salt in a bowl. Remove the chicken pieces from the marinade and pat dry with paper towels. Dredge the chicken pieces in the flour mixture and transfer to a plate.
4 Fry the chicken in batches (about 3), about 3 minutes on each side, until deep golden brown and the chicken is cooked through. (If the chicken is browning too quickly, reduce the heat a bit). Remove to a plate lined with paper towels to soak up the excess oil.