Preheat oven to 375°F. Toss together spinach and pesto in a medium bowl.
Stir together Alfredo sauce and chicken broth in another bowl. Spread one-third of Alfredo mixture (about 1/2 cup) into a lightly greased 11- x 7-inch baking dish. Top with half of spinach mixture.
Stir together cooked pasta, chicken, and remaining Alfredo mixture; spoon half of chicken mixture over spinach mixture. Repeat layers once with remaining spinach mixture and chicken mixture.
Bake in preheated oven 30 minutes. Remove from oven, and sprinkle with cheese. Return to oven, and bake until hot and bubbly, about 5 minutes. Top with basil and paprika.