Huli huli chicken will keep in the refrigerator for up to 5 days. Store it in an airtight container.
You can also freeze it. Place the raw chicken and huli huli sauce in a Ziploc bag and store it in the freezer. It will keep for up to 2 months. When you're ready to cook it, let it thaw overnight in the refrigerator and then grill it or bake it as stated in this post.