HEAT oil in large nonstick skillet on medium-high heat. Meanwhile, cut apart chicken legs and thighs. Add to skillet; cook 10 min. or until lightly browned on both sides, turning occasionally.
ADD tomatoes and tomato paste; mix well. Stir in peppers; cover. Simmer on medium-low heat 20 min. or until chicken is done (165°F), stirring occasionally.
REMOVE from heat. Stir in Parmesan; sprinkle with shredded cheese. Let stand until cheese is melted.