Preheat oven to 350°F. Drain 1 can of the tomatoes: reserve liquid. Combine the drained tomatoes and chicken in large bowl; mix well. Set aside.
Wrap tortillas in damp paper towels. Place on microwavable plate. Microwave on HIGH 45 seconds to 1 minute or until softened.
Top each tortilla with 2 tablespoons of the cheese and 1/4 cup chicken mixture; roll up. Place seam-side down in 13x9-inch baking dish. Combine the reserved tomato liquid, the remaining can of undrained tomatoes and tomato sauce; mix well. Pour evenly over tortillas; sprinkle with the remaining 1 cup cheese. Cover with aluminum foil.
Bake 30 minutes or until enchiladas are hot and cheese melts.