Cook chicken in hot oil in large skillet on medium-high heat 6 minutes on each side or until chicken is cooked through.
Remove chicken from skillet; cover to keep warm. Add water and broccoli to skillet; bring to a boil. Add stuffing mix; stir just until moistened. Return chicken to skillet; sprinkle with cheese. Reduce heat to low; cover. Cook 5 minutes or until cheese is melted.