In a medium saucepan, bring 3 cups salted water to a boil. Add the chicken
breasts, and cook for about 20 minutes. Remove from the heat, drain, and let
cool at room temperature. Shred the chicken. In a small bowl, mix the chicken
broth with the shredded chicken.Preheat the oven to 375 degrees.
In a 9-by-13-inch baking dish, spread one-third of the bechamel sauce over
the bottom, and then layer evenly with the shredded-chicken mixture, another
third of the bechamel sauce, the rice, and then the remaining bechamel sauce
in an even layer on the top.
Sprinkle on the Parmesan cheese.
Set the baking dish in the upper third of the oven. Bake until it bubbles and
the top is lightly browned, 10 to 15 minutes.