Puree pineapple, jalapeño, and garlic in a blender until almost smooth. Pour pineapple puree into a large glass baking dish. Add orange juice, lime juice, soy sauce, chopped cilantro, chopped basil, black pepper, orange peel, and lime peel to puree. Stir to combine. Add chicken to marinade and turn to coat. Cover and refrigerate for at least 4 hours, turning often.
Remove chicken from marinade. Using a rubber spatula, lightly scrape excess marinade from chicken. Strain marinade into heavy medium saucepan. Transfer ⅓ cup marinade to a small bowl and whisk in honey. Boil remaining marinade for about 15 minutes, until reduced to 1 ½ cups sauce. Whisk in butter.
Prepare a grill or fry pan over medium-high heat. Brush the grill or pan with oil. Cook chicken, turning and basting often, with reserved honey marinade for about 10 minutes. Chicken should have an internal temperature of 165° F.