In a large, deep skillet, cook chicken in 3 tablespoons teriyaki sauce on medium-high heat until just white on the outside (doesn't need to be cooked through).
Add remaining ingredients, except broccoli and extra teriyaki sauce, and bring to a boil.
Reduce heat and cover with lid. Simmer for about 20 minutes.
Add broccoli, cover again, and simmer an additional 5 minutes or until rice is cooked through.
Spoon extra teriyaki sauce, to taste, over the rice and serve immediately.
