Cook spinach as directed on package; squeeze to drain. Stir in butter; set aside.
Meanwhile, place 1 chicken breast half between 2 pieces of plastic wrap or waxed paper. Working from center, gently pound chicken with flat side of meat mallet or rolling pin until about 1/4 inch thick; remove wrap. Repeat with remaining chicken breast halves. In shallow bowl, combine bread crumbs and basil. Coat chicken breasts with crumb mixture.
Heat oil in large skillet over medium-high heat until hot. Add chicken breasts; cook 5 to 7 minutes on each side or until lightly browned, fork tender and juices run clear. Reduce heat to low. Spoon cooked spinach evenly over each chicken breast half; sprinkle with cheese. Cover; cook until cheese is melted.