In a large skillet over medium heat, heat oil. Add onion and cook until tender, 6 minutes, then add garlic and cook 1 minute. Add ground chicken and cook until no longer pink, about 6 minutes more.
Stir ketchup, brown sugar, mustard, chili powder, and Worcestershire and season with salt and pepper. Simmer until thick and saucy, 5 minutes.
Top with mozzarella and cover with lid to melt, 2 minutes.
Serve on buns.
