Cut chicken into bite sized cubes and place in a slow cooker.
Whisk together orange juice, orange zest, soy sauce, brown sugar, and rice vinegar. Pour into the slow cooker along with the garlic and ginger. Toss to coat the chicken evenly.
Close the lid and cook on low for 2 hours.
After 2 hours increase slow cooker heat to high. Whisk together the cornstarch and cold water until smooth. Pour into the slow cooker and mix evenly into the chicken and sauce, then stir in the broccoli.
Close the lid and allow to cook on high for about 30 minutes. At this point the sauce should have thickened and broccoli should be tender.
Serve over rice with green onion and more orange zest.
