If desired, remove skin from chicken. For rub, in a small bowl combine oil, garlic, salt, and red pepper. Spoon rub evenly over chicken; rub in with your fingers. For sauce, in a small saucepan combine jalapeno jelly, basil, and lime juice. Cook and stir over low heat until jelly is melted. Remove from heat.
For a charcoal grill, arrange medium-hot coals around a drip pan. Test for medium heat above the pan. Place chicken, bone side up, on grill rack over drip pan. Cover and grill for 50 to 60 minutes or until tender and no longer pink, turning once and brushing with some of the sauce during the last 5 minutes of grilling. (For a gas grill, preheat grill. Reduce heat to medium. Adjust for indirect cooking. Grill as above.) To serve, reheat and pass the remaining sauce with chicken. Makes 4 servings.