Place the chicken in the bottom of a 6-quart or larger slow cooker.
In a medium mixing bowl or very large measuring cup, whisk together the soy sauce, honey, tomato paste, chili paste, garlic, and rice vinegar.
Pour over the chicken.
Cover and cook on LOW for 4 to 5 hours or HIGH for 2 to 3 hours, until the chicken reaches an internal temperature of 165 degrees F.
Remove the chicken to a plate and let cool slightly.
Whisk the cornstarch into the slow cooker cooking liquid.
Cover and cook on HIGH for 15 minutes, until the sauce thickens slightly, stirring occasionally.
Shred the chicken and place it in the slow cooker.
Stir to coat the chicken with the sauce.
Serve over rice, sprinkled with green onions and sesame seeds.