Place chicken between 2 sheets of heavy-duty plastic wrap; flatten to 1/8-inch thickness using a meat mallet or rolling pin. Sprinkle evenly with salt and pepper; set aside.
Drain spinach well; press between layers of paper towels.
Sauté spinach and onion in a nonstick skillet coated with cooking spray over medium-high heat 3 to 4 minutes or until onion is tender. Remove from heat, and stir in cream cheese until blended. Stir in mozzarella cheese and next 5 ingredients. Spoon spinach mixture evenly on each chicken breast half; roll up, jellyroll fashion.
Unfold phyllo on a lightly floured surface. Stack 2 sheets, coating tops lightly with cooking spray between sheets. (Keep remaining sheets covered with plastic wrap.) Place 1 chicken roll on a short side of phyllo stack; gently roll up, folding in long sides. Repeat procedure with remaining phyllo sheets, cooking spray, and remaining chicken. Place a rack coated with cooking spray in a shallow baking pan; place rolls on top of rack.
Bake at 425° for 35 to 40 minutes or until chicken is done.