In a small bowl, combine first 8 ingredients. With a spoon or a basting brush, spread seasoning paste over the chicken.
Grill chicken using medium heat for a gas grill or indirect heat for a charcoal grill. Close the lid and grill until chicken reaches 180 degrees F in the thighs and 170 degrees F in the breast, about 30 minutes.
In a small bowl, combine all lime butter ingredients.
Drizzle over chicken just before serving or serve separately for dipping.