Heat oil in a large skillet over medium heat; add chicken.
Brown chicken 3 to 4 minutes; place in a 5- or 6-quart slow cooker.
Top chicken with onion.
Whisk together pineapple juice, tomato paste, soy sauce and vinegar; pour over chicken.
Cover and cook on Low 5 to 6 hours; remove chicken from slow cooker and shred with 2 forks.
Stir cornstarch into sauce in slow cooker; increase slow cooker heat to High and cook, uncovered, 30 minutes or until sauce thickens slightly.
Spoon chicken onto buns; top with sauce.
Serve pineapple chunks and carrots with sandwiches if using.