Heat oven to 425°F. Make pie crusts as directed on box for Two-Crust Pie, using 9-inch glass pie plate.
In 2-quart saucepan, melt butter over medium-low heat. Stir in flour and pepper; cook until mixture is smooth and bubbly. Gradually add broth and milk, stirring constantly, until mixture boils and thickens.
Add cheese; stir until melted. Stir in chicken and broccoli. Pour mixture into crust-lined pie plate. Top with second crust; seal edge and flute. Cut slits in several places in top crust.
Bake 30 to 35 minutes or until crust is golden brown and filling is bubbly. Cover edge of crust with strips of foil after first 15 to 20 minutes of baking to prevent excessive browning. Cool 10 minutes before serving.