In a large re-sealable plastic bag, combine limejuice, rum, soy sauce, Worcestershire sauce, and garlic. Cut chicken into bite-sized pieces, about 2 inches long. Add chicken to marinade bag, then close and turn bag to make sure all chicken pieces are coated in the mixture. Refrigerate at least 1 hour. Remove chicken from refrigerator and set aside.
In a shallow dish, combine flour, paprika, salt, and pepper. In a large Dutch oven or heavy-bottomed skillet, heat 1 to 2 inches of oil over medium-high heat.
Pour off excess marinade from chicken. Pat chicken dry and coat with seasoned flour, shaking off the excess. Gently place in hot oil, being careful not to overcrowd the pan. Fry 4 to 5 minutes per side, until golden brown and crispy. Drain on paper towel-lined platter and serve hot.