In large container with lid, or in large zip-top bag, mix together chicken, mojo, nectar and adobo until coated; transfer to refrigerator. Marinate chicken at least 2 hrs, or up to 24 hours.
Strain chicken, discarding marinade. On each skewer, alternately thread pineapple, chicken, onions and peppers.
Prepare grill to medium-high heat (or, heat oil in large grill pan over medium-high heat). Cook skewers, turning once, until chicken turns dark golden brown and cooked through and vegetables are tender, about 15 minutes. Transfer to serving platter; serve warm.