Preheat the oven to 350°F (175°C) and lightly spray a 9-inch pie plate with cooking spray; set aside.
Cook the spaghetti according to package directions until al dente, then drain well in a colander.
Transfer the drained spaghetti to a large bowl and toss with the 2 eggs and 4 tablespoons (about 1/4 cup) of the Parmesan until evenly coated.
Press the spaghetti mixture firmly into the bottom and up the sides of the prepared pie plate to form a crust.
In a bowl, combine the chopped cooked chicken, the 10-oz jar of Alfredo sauce, and 1/4 cup of the shredded mozzarella; mix until combined.
Spread the chicken and Alfredo mixture evenly into the spaghetti crust.
Top with the remaining mozzarella and the remaining Parmesan cheese.
Bake for 30 to 40 minutes, until the filling is heated through and the cheese is melted and bubbly.
Let the pie stand for 10 minutes before slicing and serving to help it set.