Combine first 3 ingredients in a large bowl; set aside.
Bring brown sugar and syrup to a boil in a small saucepan over medium-high heat, stirring constantly; remove from heat. Stir in peanut butter and vanilla until blended.
Pour peanut butter mixture over cereal mixture, stirring until coated; let stand 10 minutes. Stir in chocolate morsels. Press mixture into a 13- x 9-inch pan; cool in pan on a wire rack. Cut into bars.