Preheat oven to 400°F (200°C). Scrub potatoes and bake for 45–60 minutes until fork-tender.
Mix shredded chicken with BBQ sauce in a bowl.
Slice baked potatoes open, fluff insides with a fork, and stuff with BBQ chicken.
Top with cheddar and mozzarella, then return to oven for 5–10 minutes to melt cheese.
Sprinkle with green onions and add sour cream before serving.