MELT butter in large skillet on medium heat. Add onions; cook and stir 3 to 5 min. or until crisp-tender. Add chicken, spinach and pesto; cook 5 min. or until heated through, stirring frequently.
ADD broth and milk; stir. Bring to boil. Stir in rice; simmer on medium-low heat 5 min.
REMOVE from heat. Stir in cheese; cover. Let stand 5 min.