Place the chicken breasts in the bottom of the slow cooker.
Add the broccoli florets, sliced red bell pepper, and sliced carrots on top of the chicken.
In a small bowl, stir together the sweet chili sauce, soy sauce, minced garlic, and grated ginger.
Pour the sauce mixture evenly over the chicken and vegetables.
Cover and cook on low until the chicken reaches an internal temperature of 165°F and the vegetables are tender.
Remove the chicken, shred or slice it, and return it to the slow cooker. Stir everything to coat with the sauce.
Serve over cooked rice and top with chopped green onions.