Bring a large pot of water to a boil. Stir in a generous amount of salt, then add the pasta. Give it a stir to ensure that none of the pieces are sticking together. Cook according to package directions, then drain.
Return the pasta to the pot, then add the pesto sauce. Mix well so that the oil from the pesto thoroughly coats the pasta. Place over medium-low heat if using jarred sauce so that it will warm up and not make the pasta cold.
Add the Alfredo sauce then mix well. Add shredded chicken and cheese then serve.